Shifted poly-Cauchy numbers
نویسندگان
چکیده
منابع مشابه
Explicit formulae for sums of products of Cauchy numbers including poly-Cauchy numbers
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. I...
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 کاملThe Cauchy numbers
We study many properties of Cauchy numbers in terms of generating functions and Riordan arrays and find several new identities relating these numbers with Stirling, Bernoulli and harmonic numbers. We also reconsider the Laplace summation formula showing some applications involving the Cauchy numbers.
متن کاملPoly-Cauchy polynomials
We introduce the poly-Cauchy polynomials which generalize the classical Cauchy polynomials, and investigate their arithmetical and combinatorial properties. These polynomials are considered as analogues of the poly-Bernoulli polynomials that generalize the classical Bernoulli polynomials. Moreover, we investigate the zeta functions which interpolate the poly-Cauchy polynomials. The values of th...
متن کاملShifted Jacobi Polynomials and Delannoy Numbers
We express a weighted generalization of the Delannoy numbers in terms of shifted Jacobi polynomials. A specialization of our formulas extends a relation between the central Delannoy numbers and Legendre polynomials, observed over 50 years ago [12, 17, 19], to all Delannoy numbers and certain Jacobi polynomials. Another specialization provides a weighted lattice path enumeration model for shifte...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Lithuanian Mathematical Journal
سال: 2014
ISSN: 0363-1672,1573-8825
DOI: 10.1007/s10986-014-9235-y