Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-19T15:49:45.455686Z
Paper Citation Record · LEDGER
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions
As of 20 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 1 inbound Pith citation observation for arXiv:2605.15386.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-13T02:35:57.683233Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
50 of 50 outbound references displayed
- verified exact1
- verified fuzzy22
- unresolved27
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 6ae1568d-dae1-4d7e-9e95-5747927cc133 · outbound
This paper cites and Tricomi, F.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and Tricomi, F
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.037014Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 7a01963f-0144-493c-aa5a-9492ec833d94 · outbound
This paper cites On the efficient calculation of a linear combination of chi-square random variables with an appli- cation in counting string vacua.J.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions On the efficient calculation of a linear combination of chi-square random variables with an appli- cation in counting string vacua.J
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.051272Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a76f6ad1-8bc5-4216-bb4c-bc6e3f4b339e · outbound
This paper cites and L´ opez-Bl´ azquez, F.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and L´ opez-Bl´ azquez, F
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.070811Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 24e141af-593b-4add-bfbb-bf774dadf319 · outbound
This paper cites and L´ opez-Bl´ azquez, F.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and L´ opez-Bl´ azquez, F
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.108143Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 6e791cef-fe5c-4cde-95ae-50f855c8aa37 · outbound
This paper cites Right-tail asymptotics for products of independent normal random variables.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Right-tail asymptotics for products of independent normal random variables
Reference 5
- Resolution
- verified exact
- local_arxiv, observed 2026-05-19T15:52:38.092471Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a89746a7-201e-46c2-8fca-77d71f93930f · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.104572Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation cdfe7341-bbbd-4949-a4bc-3ba9160a9d2a · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.099131Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ae3e7559-251b-4784-8367-c0ca3f32c778 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.102998Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation dd48c0e6-9967-4385-b29c-a26e0e0f9278 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.093680Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b919b297-949e-4af5-a42c-401b203b2f08 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.095547Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8386e320-a59a-4b86-800d-86fd43708bef · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.097474Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 0f0f6502-47e6-430c-aa25-4c05ed97bdf1 · outbound
This paper cites E., Nadarajah, S.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions E., Nadarajah, S
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.106415Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 1644ce24-5072-40d4-85f8-623de4217815 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.079889Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ae07eefc-b8d7-4dc5-ab95-e970ccc76b40 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.049335Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9f4f3a61-7b14-49e4-8701-59058befc9e1 · outbound
This paper cites and Temme, N.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and Temme, N
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.056895Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 36b0597f-fc5f-43fa-8682-aca05c32868a · outbound
This paper cites and Temme, N.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and Temme, N
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.053196Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 0d21ebc6-49f0-4dd3-8bfa-c39ec0ec46d3 · outbound
This paper cites and Temme, N.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and Temme, N
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.042305Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ae667cd2-13da-4f22-8eec-fe838d406be6 · outbound
This paper cites and Pog´ any, T.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and Pog´ any, T
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.044184Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 864d4fc9-90cd-4f59-9a8c-ea20121c40e8 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.047635Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation edd5c0a0-fb5d-475b-a097-395bb85ba7e1 · outbound
This paper cites Distribution of definite and of indefinite quadratic forms.Ann.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Distribution of definite and of indefinite quadratic forms.Ann
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.038801Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b68d13b4-ce5c-4b57-a5c5-b9de8220cf0b · outbound
This paper cites and Hanˇ c, J.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and Hanˇ c, J
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.033580Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 19c63bd8-2bb5-4d8f-b6ce-ed7dd489fee5 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.031663Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e6a3e96b-1803-4157-a4b5-09bbddffd6b4 · outbound
This paper cites and Alouini, M.–S.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and Alouini, M.–S
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.035289Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9adcfb57-9964-46f8-a960-55b9531eb279 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.040549Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation aed9bc0d-b341-4632-b05d-9d802d33f42c · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.045945Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f4a21659-439f-4192-bbc3-24fb902f6fe5 · outbound
This paper cites L., Kotz, S.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions L., Kotz, S
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.028271Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b68111c8-49aa-4c90-8f55-4922152fd5ca · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.058600Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 754bce70-52fc-42eb-9042-38a1fcced265 · outbound
This paper cites A note on gamma difference distributions.J.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions A note on gamma difference distributions.J
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.026565Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation aad824ad-5321-4f6c-ae3d-02d40cecebc5 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.021159Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 304a9728-b493-4250-b0a6-4fc237f10eb5 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.019488Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 2b61ce4b-0efa-428f-9bc1-467dac7df01b · outbound
This paper cites and Bablok, B.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and Bablok, B
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.023128Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 886dfa1f-3c26-45b1-927a-3f5ce9d4273d · outbound
This paper cites and Zov´ e, R.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and Zov´ e, R
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.024775Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 0e779ea7-cdc3-43c9-9fff-3061ad3d0bcf · outbound
This paper cites and Schober, R.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and Schober, R
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.067148Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 7b2d7b61-8357-4039-9d8e-b2c796b1d75b · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.029919Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ae8b1633-262c-488f-a868-05d8344d5d54 · outbound
This paper cites L., Wang, X., Yeh, S.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions L., Wang, X., Yeh, S
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.055168Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e2bc4a0b-f38e-43df-ad44-fdfb28768102 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.074345Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 61973e0f-1963-4476-bbd1-8a0390aeda82 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 37
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.088645Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a1f32788-6f5b-40a1-a447-5c1cabb8b74c · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.085032Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation c7a30729-fe15-4652-8865-4dcea5e83179 · outbound
This paper cites Wiley.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Wiley
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.090299Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 80b0a99d-6bc7-4e00-9d40-557235ff533f · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 40
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.086974Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 61972467-bc6d-4111-b3db-fecb46620a32 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 41
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.092001Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation c42dc46a-18f7-4a91-9746-66ef3e4027b4 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 42
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.109839Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 84fb7c46-4423-4465-98fd-8a0225ace32e · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 43
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.081628Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation efb9613e-3173-4fbb-9e40-83e1eea53175 · outbound
This paper cites B., Brychkov, Y.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions B., Brychkov, Y
Reference 44
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.083311Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 6146894a-05ed-4f9f-b1d4-231e17c0206a · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 45
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.101342Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 0355f8e1-09ba-4d75-9f8b-1f2db74916cc · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 46
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.076274Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 74cb330c-6330-465e-914c-0f1e885c6a95 · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 47
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.069018Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 5187a1df-612f-4b8d-a822-82b3c0e8843e · outbound
This paper cites and Usseglio-Carleve A.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and Usseglio-Carleve A
Reference 48
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.072579Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 2633011f-40aa-49e8-a81a-ead88945fccc · outbound
This paper cites an unresolved cited work.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions Unresolved cited work
Reference 49
- Resolution
- unresolved
- raw_fallback, observed 2026-05-19T15:52:39.078007Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 17248ee8-dbd2-4ae0-a39f-c6b85055d7ce · outbound
This paper cites and Bartlett, M.
The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions and Bartlett, M
Reference 50
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-19T15:52:39.060331Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Pith citing papers
Observation 0e251785-850f-4998-8bbd-24e1b579c8ed · inbound
Log-convexity and log-concavity of noncentral gamma sums and differences cites this paper.
Log-convexity and log-concavity of noncentral gamma sums and differences The non-central gamma sum and difference distributions: exact distribution and asymptotic expansions
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-07-13T02:35:57.683233Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.