Tokyo Journal of Mathematics

Truncated Bernoulli-Carlitz and Truncated Cauchy-Carlitz Numbers

Takao KOMATSU

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Abstract

In this paper, we define the truncated Bernoulli-Carlitz numbers and the truncated Cauchy-Carlitz numbers as analogues of hypergeometric Bernoulli numbers and hypergeometric Cauchy numbers, and as extensions of Bernoulli-Carlitz numbers and the Cauchy-Carlitz numbers. These numbers can be expressed explicitly in terms of incomplete Stirling-Carlitz numbers.

Article information

Source
Tokyo J. Math., Volume 41, Number 2 (2018), 541-556.

Dates
First available in Project Euclid: 20 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1511221571

Mathematical Reviews number (MathSciNet)
MR3908809

Zentralblatt MATH identifier
07053491

Subjects
Primary: 11R58: Arithmetic theory of algebraic function fields [See also 14-XX]
Secondary: 11T55: Arithmetic theory of polynomial rings over finite fields 11B68: Bernoulli and Euler numbers and polynomials 11B73: Bell and Stirling numbers 11B75: Other combinatorial number theory 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 05A19: Combinatorial identities, bijective combinatorics

Citation

KOMATSU, Takao. Truncated Bernoulli-Carlitz and Truncated Cauchy-Carlitz Numbers. Tokyo J. Math. 41 (2018), no. 2, 541--556. https://projecteuclid.org/euclid.tjm/1511221571


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