Explicit formulae for sums of products of Cauchy numbers including poly-Cauchy numbers
نویسنده
چکیده
Recently, K. Kamano studied sums of products of Bernoulli numbers including poly-Bernoulli numbers. A relation among these sums was given, and an explicit expression of sums of two products was also given, reduced to the famous Euler’s formula. The concept of poly-Cauchy numbers is given by the author as a generalization of the classical Cauchy number and an analogue of poly-Bernoulli number. In this paper, we investigate sums of products of Cauchy numbers including poly-Cauchy numbers in order to give explicit expressions in any m products. §
منابع مشابه
Sums of Products of Bernoulli Numbers, Including Poly-Bernoulli Numbers
We investigate sums of products of Bernoulli numbers including poly-Bernoulli numbers. A relation among these sums and explicit expressions of sums of two and three products are given. As a corollary, we obtain fractional parts of sums of two and three products for negative indices.
متن کاملAlgebraic aspects of increasing subsequences
We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest increasing subsequence of a random involution with constrained number of fixed points; new formulae for partial Cauchy-Littlewood sums, as well as new proofs of old f...
متن کاملPoly-Cauchy Numbers and Polynomials with Umbral Calculus Viewpoint
In this paper, we give some interesting identities of poly-Cauchy numbers and polynomials arising from umbral calculus.
متن کاملHigher-order Cauchy of the First Kind and Poly-cauchy of the First Kind Mixed Type Polynomials
In this paper, we study higher-order Cauchy of the first kind and poly-Cauchy of the first kind mixed type polynomials with viewpoint of umbral calculus and give some interesting identities and formulae of those polynomials which are derived from umbral calculus.
متن کاملThe inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter
We investigate the interior of regular axisymmetric and stationary black holes surrounded by matter and find that for non-vanishing angular momentum of the black hole the spacetime can always be extended regularly up to and including an inner Cauchy horizon. We provide an explicit relation for the regular metric at the inner Cauchy horizon in terms of that at the event horizon. As a consequence...
متن کامل