NDLI: A Note on the Asymptotic Expansion of a Ratio of Gamma Functions

Content Provider	Scilit
Author	Fields, Jerry L.
Copyright Year	1966
Description	Many problems in mathematical analysis require a knowledge of the asymptotic behaviour of Γ(z + α)/Γ(z + β) for large values of \|z\|, where α and β are bounded quantities. Tricomi and Erdélyi in (1), gave the asymptotic expansion where the are the generalised Bernoulli polynomials, see (2), defined by In this note, we show that if, instead of considering z to be the large variable, we consider a related large variable, (1) can be improved from a computational viewpoint.
Related Links	https://www.cambridge.org/core/services/aop-cambridge-core/content/view/43C8615C6E3A446BBE8714857141E43D/S0013091500013171a.pdf/div-class-title-a-note-on-the-asymptotic-expansion-of-a-ratio-of-gamma-functions-div.pdf
Ending Page	45
Page Count	3
Starting Page	43
ISSN	00130915
e-ISSN	14643839
DOI	10.1017/s0013091500013171
Journal	Proceedings of the Edinburgh Mathematical Society
Issue Number	1
Volume Number	15
Language	English
Publisher	Cambridge University Press (CUP)
Publisher Date	1966-06-01
Access Restriction	Open
Subject Keyword	Proceedings of the Edinburgh Mathematical Society Mathematical Physics Asymptotic Expansion
Content Type	Text
Subject	Mathematics

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A Note on the Asymptotic Expansion of a Ratio of Gamma Functions