Paper Citation Record · LEDGER

Operational vs. Umbral Methods and Borel Transform

As of 16 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 0 inbound Pith citation observations for arXiv:1908.04160.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
1908.04160 v1

Coverage vector

measured 39 of 39 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:57:57.387533Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

39 of 39 outbound references displayed

verified exact1
verified fuzzy35
unresolved2
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

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Outbound references

Observation 0d6bebd1-be35-4495-8d42-6a61dd5a7139 · outbound

This paper cites The Fractional Calculus: Theory an d Applications of Di ﬀerentiation and Integration to Arbitrary Order.

Operational vs. Umbral Methods and Borel Transform The Fractional Calculus: Theory an d Applications of Di ﬀerentiation and Integration to Arbitrary Order

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:58.227758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fed7c548-1d1f-4b50-be1c-ac6c7dc8534a · outbound

This paper cites Appl Math and Comp.

Operational vs. Umbral Methods and Borel Transform Appl Math and Comp

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:58.206427Z

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Observation 412cb490-c43e-4a65-9be4-a1c495bbbaa4 · outbound

This paper cites Fonctions Hypergeometriques and Hyperspheriques.

Operational vs. Umbral Methods and Borel Transform Fonctions Hypergeometriques and Hyperspheriques

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:58.183309Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d6a2fffd-eb1a-42d9-9c67-d4e6036cea18 · outbound

This paper cites Mathematical Me thods for Physics.

Operational vs. Umbral Methods and Borel Transform Mathematical Me thods for Physics

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:58.165916Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation aa59a5c6-1796-48dd-8825-156ed39749e2 · outbound

This paper cites On Ramanujan Master Theorem.

Operational vs. Umbral Methods and Borel Transform On Ramanujan Master Theorem

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-14T13:57:57.178364Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 166cee06-ebee-4f23-a6e5-2ceb00944e03 · outbound

This paper cites Heisenberg algebra, umb ral calculus and orthogonal polynomials.

Operational vs. Umbral Methods and Borel Transform Heisenberg algebra, umb ral calculus and orthogonal polynomials

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:58.146511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 36cc1de2-7254-4c1d-8abb-28a0c8ba8e64 · outbound

This paper cites Symbolic methods fo r the evaluation of sum rules of Bessel functions.

Operational vs. Umbral Methods and Borel Transform Symbolic methods fo r the evaluation of sum rules of Bessel functions

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:58.127811Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 487bb009-d618-4c14-b4ec-f7bea4caca1c · outbound

This paper cites Umbral Calculus, a Different Mathematical Language.

Operational vs. Umbral Methods and Borel Transform Umbral Calculus, a Different Mathematical Language

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-14T13:57:57.201730Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c58ea7e-1173-4a37-955b-ddf2abab7b3f · outbound

This paper cites The Umbral Calculus.

Operational vs. Umbral Methods and Borel Transform The Umbral Calculus

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:58.111306Z

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Observation 0e782221-aab3-4d39-9e9d-b566523ebef1 · outbound

This paper cites Ramanujan’s Notebooks.

Operational vs. Umbral Methods and Borel Transform Ramanujan’s Notebooks

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:58.091925Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0268dc30-aa12-4cbb-ab88-ab047f678242 · outbound

This paper cites The spherical Bess el and Struve functions and operational methods.

Operational vs. Umbral Methods and Borel Transform The spherical Bess el and Struve functions and operational methods

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:58.075286Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation bd285c99-3d1e-4cf4-bc24-1ba93a77d3cd · outbound

This paper cites On evaluation of integrals involving Bessel functions.

Operational vs. Umbral Methods and Borel Transform On evaluation of integrals involving Bessel functions

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-14T13:57:57.484435Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5be23d34-af32-42bc-838b-e659a2c9db67 · outbound

This paper cites Integral transforms and operationalcalculus.

Operational vs. Umbral Methods and Borel Transform Integral transforms and operationalcalculus

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:58.057929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5a822d33-8acb-42e7-9bb4-114ee0198f68 · outbound

This paper cites Generalized polynomials, operational iden tities and their applications.

Operational vs. Umbral Methods and Borel Transform Generalized polynomials, operational iden tities and their applications

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:58.040863Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5fbecd69-dbea-4e3b-82ce-b19d2c82c30c · outbound

This paper cites Operational versus umbral methods and the Borel transform.

Operational vs. Umbral Methods and Borel Transform Operational versus umbral methods and the Borel transform

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:58.022730Z

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Observation 06ffea0c-8883-4b29-8d66-8c9daabe11d2 · outbound

This paper cites The Euler Legacy to Modern Physi cs.

Operational vs. Umbral Methods and Borel Transform The Euler Legacy to Modern Physi cs

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:58.003036Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 791d3939-d282-4265-ba9e-19f4ab30bb32 · outbound

This paper cites Critical Properties of φ4 Theories.

Operational vs. Umbral Methods and Borel Transform Critical Properties of φ4 Theories

Reference 17

Resolution: malformed identifier; no resolver link, observed 2026-08-14T13:57:57.260486Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe44d5f6-438e-4134-8067-4ffaba915b6b · outbound

This paper cites Zeta Regularizations with Applica tions.

Operational vs. Umbral Methods and Borel Transform Zeta Regularizations with Applica tions

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.984300Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fea0e93f-44f8-403d-b78e-e493255e1cd1 · outbound

This paper cites Le cons sur les S´ eries Divergentes, Gauthier- Villars.

Operational vs. Umbral Methods and Borel Transform Le cons sur les S´ eries Divergentes, Gauthier- Villars

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.965869Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9ab9a330-9b59-4642-a795-52be7a387f96 · outbound

This paper cites Divergent Series, Clarendon Press.

Operational vs. Umbral Methods and Borel Transform Divergent Series, Clarendon Press

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.940309Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5972dbd7-c73b-4ae4-a093-588777116eaa · outbound

This paper cites A note on truncated p olynomials.

Operational vs. Umbral Methods and Borel Transform A note on truncated p olynomials

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.922680Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7879bf7f-466e-445a-b84d-114efcc4e0f7 · outbound

This paper cites Lacunary Generati ng Functions for the Laguerre Polynomials.

Operational vs. Umbral Methods and Borel Transform Lacunary Generati ng Functions for the Laguerre Polynomials

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.906266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5a51f823-36b7-4156-89d8-0f7122809cc7 · outbound

This paper cites Summation of divergent series: Order-d ependent mapping.

Operational vs. Umbral Methods and Borel Transform Summation of divergent series: Order-d ependent mapping

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.887002Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6579dbc4-29f5-4725-a7da-5335dc9fa1a0 · outbound

This paper cites Special Functions For Engeneers and Applie d mathematicians.

Operational vs. Umbral Methods and Borel Transform Special Functions For Engeneers and Applie d mathematicians

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.869640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5bb3e300-1409-4d8f-a846-118e0ed74a5b · outbound

This paper cites Une g´ en´ eralisation de l’int´ egrale de Laplace-Abel.

Operational vs. Umbral Methods and Borel Transform Une g´ en´ eralisation de l’int´ egrale de Laplace-Abel

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.853157Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1cb26170-91a3-42b1-b184-1903ef1cd3d2 · outbound

This paper cites A triple lacunary generating func tion for Hermite polynomials.

Operational vs. Umbral Methods and Borel Transform A triple lacunary generating func tion for Hermite polynomials

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.834937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ce6c6327-47b9-49a0-8d87-393d015a110f · outbound

This paper cites The heat equation.

Operational vs. Umbral Methods and Borel Transform The heat equation

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.818608Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 25bf5699-3af4-400b-9f2d-b9bea0a7f094 · outbound

This paper cites Applications of the classical umbral calculu s.

Operational vs. Umbral Methods and Borel Transform Applications of the classical umbral calculu s

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.802260Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a120c8fb-7048-414a-8b81-4f314321fcb8 · outbound

This paper cites Motzkin numbe rs: an operational point of view.

Operational vs. Umbral Methods and Borel Transform Motzkin numbe rs: an operational point of view

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.775860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a65ebde3-9630-4903-b04b-400fafb24190 · outbound

This paper cites On an umbral tre atment of Gegenbauer, Legendre and Jacobi polynomials.

Operational vs. Umbral Methods and Borel Transform On an umbral tre atment of Gegenbauer, Legendre and Jacobi polynomials

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.754972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3bfb3e65-394f-4fed-bde1-3e9490958c47 · outbound

This paper cites The higher-order heat-type equations via signed L´ evy stable and generalize d Airy functions.

Operational vs. Umbral Methods and Borel Transform The higher-order heat-type equations via signed L´ evy stable and generalize d Airy functions

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.736685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8226d05b-22b7-443e-a7b8-5a8bebd2ea14 · outbound

This paper cites Recherches sur les polynomes d’Hermite.

Operational vs. Umbral Methods and Borel Transform Recherches sur les polynomes d’Hermite

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.718398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9bd76432-ad1b-4807-b340-06b5fc7b8937 · outbound

This paper cites Hermite Calcul us.

Operational vs. Umbral Methods and Borel Transform Hermite Calcul us

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.699309Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 49249c83-1242-490e-bcfd-510af82513d9 · outbound

This paper cites Theory of Communication, Part 1.

Operational vs. Umbral Methods and Borel Transform Theory of Communication, Part 1

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.676390Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0c574000-ca00-44b7-a266-aa13f11cbf55 · outbound

This paper cites The History of Blissard’s Symbolic Method, wit h a Sketch of its Inventor’s Life.

Operational vs. Umbral Methods and Borel Transform The History of Blissard’s Symbolic Method, wit h a Sketch of its Inventor’s Life

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.646784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation db306aab-30bb-4a1c-b645-84eefe37a3ba · outbound

This paper cites On generalized heat polynomials.

Operational vs. Umbral Methods and Borel Transform On generalized heat polynomials

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.616610Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e0c3c0b3-e1d9-4bf4-8358-20c866817e53 · outbound

This paper cites Expansions in terms of heat po lynomials and associated functions.

Operational vs. Umbral Methods and Borel Transform Expansions in terms of heat po lynomials and associated functions

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.597720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b0a56c36-8e65-4f91-bc8c-b971563b431a · outbound

This paper cites Funzioni Speciali.

Operational vs. Umbral Methods and Borel Transform Funzioni Speciali

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.576476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 871b0467-0563-49d0-a402-5d4850da31f4 · outbound

This paper cites Theory of General ized Trigonometric functions: From Laguerre to Airy forms.

Operational vs. Umbral Methods and Borel Transform Theory of General ized Trigonometric functions: From Laguerre to Airy forms

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T13:57:57.553947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

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