Padé Approximations and Irrationality Measures on Values of Confluent Hypergeometric Functions-Reference-Cited by-同舟云学术

Padé Approximations and Irrationality Measures on Values of Confluent Hypergeometric Functions

Published:2024-08-15 Issue:16 Volume:12 Page:2516
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Hu Jiaxin¹,Yu Chenglong²^ORCID,Zhou Kangyun³

Affiliation:

1. Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 999077, China

2. Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China

3. Qiuzhen College, Tsinghua University, Beijing 100084, China

Abstract

Padé approximations are approximations of holomorphic functions by rational functions. The application of Padé approximations to Diophantine approximations has a long history dating back to Hermite. In this paper, we use the Maier–Chudnovsky construction of Padé-type approximation to study irrationality properties about values of functions with the form f(x)=∑k=0∞xkk!(bk+s)(bk+s+1)⋯(bk+t), where b,t,s are positive integers and obtain upper bounds for irrationality measures of their values at nonzero rational points. Important examples includes exponential integral, Gauss error function and Kummer’s confluent hypergeometric functions.

Funder

Tsinghua University Dushi Program

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/16/2516/pdf

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