We define a special function related to the digamma function and use it to evaluate in closed form various series involving binomial coefficients and harmonic numbers.
In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's...In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's formula and Lerch's functional equation.As applications of the result,some well-known reciprocity formulas are deduced as special cases.展开更多
文摘We define a special function related to the digamma function and use it to evaluate in closed form various series involving binomial coefficients and harmonic numbers.
基金Supported by the Natural Science Foundation of Sichuan Province(No.2023NSFSC0065)。
文摘In this paper,we study the generalized Dedekind Rademacher sums considered by Hall,Wilson and Zagier.We establish a new formula for the products of two Bernoulli functions by using Parseval's formula,Hurwitz's formula and Lerch's functional equation.As applications of the result,some well-known reciprocity formulas are deduced as special cases.
