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Padé Approximations and Irrationality Measures on Values of Confluent Hypergeometric Functions

Author

Listed:
  • Jiaxin Hu

    (Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 999077, China
    These authors contributed equally to this work.)

  • Chenglong Yu

    (Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China
    These authors contributed equally to this work.)

  • Kangyun Zhou

    (Qiuzhen College, Tsinghua University, Beijing 100084, China
    These authors contributed equally to this work.)

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 ∞ x k k ! ( b k + s ) ( b k + s + 1 ) ⋯ ( b k + 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.

Suggested Citation

  • Jiaxin Hu & Chenglong Yu & Kangyun Zhou, 2024. "Padé Approximations and Irrationality Measures on Values of Confluent Hypergeometric Functions," Mathematics, MDPI, vol. 12(16), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2516-:d:1456710
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