In this paper, we construct trigonometric functions in the form of a sum T p (h, k) which is
referred to as a Dedekind-type DC-(Dahee and Changhee) sum. We establish analytic …

In this paper we consider transformation formulas for\[B\left (z, s:\chi\right)=\sum\limits_ {m=
1}^{\infty}\sum\limits_ {n= 0}^{\infty}\chi (m)\chi (2n+ 1)\left (2n+ 1\right)^{s-1} e^{\pi im (2n+ 1) …

We introduce vast generalizations of the Hardy–Berndt sums. They involve higher-order
Euler and/or Bernoulli functions, in which the variables are affected by certain linear shifts …

In this paper, we present the character analogue of the Boole summationformula. Using this
formula, an integral representation is derived for thealternating Dirichlet $ L $-function and …

In this paper, a transformation formula under modular substitutions is derived for a large
class of generalized Eisenstein series. Appearing in the transformation formulae are …

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On Reciprocity Formulas for Apostol’s Dedekind Sums and Their Analogues Page 1 23 11
Article 14.5.4 Journal of Integer Sequences, Vol. 17 (2014), 2 3 6 1 47 On Reciprocity …

In this paper, transformation formulas for the function A_ 1\left (z, s: χ\right)= ∑\limits _ n= 1^
∞ ∑\limits _ m= 1^ ∞ χ\left (n\right) χ\left (m\right)\left (-1\right)^ mn^ s-1 e^ 2 π imnz/k A 1 z …

In this paper, we derive a formula on the integral of products of the higher-order Euler
polynomials. By the same method, similar relations are obtained for $ l $ higher-order …

In this paper, we define generalized Hardy-Berndt sums and elliptic analogue of the
generalized Hardy-Berndt sums related to elliptic Bernoulli polynomials. We give relations …