REVIEW 2 cited by
Ap\'ery Acceleration of Continued Fractions
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
We explain in detail how to accelerate continued fractions (for constants as well as for functions) using the method used by R.~Ap\'ery in his proof of the irrationality of $\zeta(3)$. We show in particular that this can be applied to a large number of continued fractions which can be found in the literature, thus providing a large number of new continued fractions. As examples, we give a new continued fraction for $\log(2)$ and for $\zeta(3)$, as well as a simple proof of one due to Ramanujan.
Forward citations
Cited by 2 Pith papers
-
Continued Fractions and Irrationality Measures for Chowla--Selberg Gamma Quotients
New continued fractions yield the first proved reasonable irrationality measures for Chowla–Selberg gamma quotients, including μ(CS(-3)) < 5.548 and μ(CS(-163)) < 2.477.
-
Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary
A theory-plus-dictionary of polynomial-type continued fractions with explicit convergence rates and Apéry-style accelerations, mostly new or newly quantified.
Discussion (0). Continue with ORCID to comment.