HYPERGEOMETRIC CAUCHY NUMBERS
HYPERGEOMETRIC CAUCHY NUMBERS
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DOI：
10.1142/s1793042112501473
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发表时间：
2013-04
影响因子：
0.7
通讯作者：
T. Komatsu
中科院分区：
文献类型：
--
作者：
T. Komatsu
For a positive integer N, define hypergeometric Cauchy numbers cN,n by $$\frac{1}{{}_2 F_1(1, N; N + 1;-x)}=\sum_{n=0}^{\infty}c_{N,n}\frac{x^n}{n!},$$ 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 $$\frac{1}{{}_1 F_1(1;N+1;x)}=\sum_{n=0}^{\infty} B_{N,n}\frac{x^n}{n!},$$ where 1F1(a;b;z) is the confluent hypergeometric function.
For a positive integer N, define hypergeometric Cauchy numbers cN,n by $$\frac{1}{{}_2 F_1(1, N; N + 1;-x)}=\sum_{n=0}^{\infty}c_{N,n}\frac{x^n}{n!},$$ 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 $$\frac{1}{{}_1 F_1(1;N+1;x)}=\sum_{n=0}^{\infty} B_{N,n}\frac{x^n}{n!},$$ where 1F1(a;b;z) is the confluent hypergeometric function.