Takao Komatsu

HYPERGEOMETRIC CAUCHY NUMBERS

For a positive integer N, define hypergeometric Cauchy numbers cN,n by

Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers

\frac{1}{{}_2 F_1(1, N; N + 1;-x)}=\sum_{n=0}^{\infty}c_{N,n}\frac{x^n}{n!},

More properties on multi-poly-Euler polynomials

where 2 F1(a, b;c;z) is the Gauss hypergeometric function. When N = 1, c1,n = cn are classical Cauchy numbers. In this paper we shall consider sums of products of hypergeometric Cauchy numbers. We note that hypergeometric Cauchy numbers are analogous to hypergeometric Bernoulli numbers BN,n defined by

ON THE CHARACTERISTIC WORD OF THE INHOMOGENEOUS BEATTY SEQUENCE

\frac{1}{{}_1 F_1(1;N+1;x)}=\sum_{n=0}^{\infty} B_{N,n}\frac{x^n}{n!},

Sums of Products of Cauchy Numbers, Including Poly-Cauchy Numbers

where 1F1(a;b;z) is the confluent hypergeometric function.

An algorithm of infinite sums representations and Tasoev continued fractions

Abstract The Fibonacci Zeta functions are defined by . Several aspects of the function have been studied. In this article we generalize the results by Ohtsuka and Nakamura, who treated the partial infinite sum for all positive integers n.