This is a collection of definite integrals involving the logarithmic and polynomial functions in terms special fundamental constants. All results this work are new.

This paper contains new explicit computations of some integrals containing elementary functions, such as powers, logarithms, exponentials. In this work the authors use their contour integral method to derive a double connected modified Bessel function second kind $K_{\nu}(z)$ and express it in terms Lerch function. A table pairs is given for interested readers. The majority results are new.

The Lerch zeta function is defined by a Dirichlet series depending on two fixed parameters. In the paper, we consider approximation of analytic functions discrete shifts function, and prove that, for arbitrary parameters step arithmetic progression, there closed non-empty subset space in critical strip such that its can be approximated function. set those infinite, it has positive density. For ...

We obtain some well-known expansions for the Lerch transcendent and the Hurwitz zeta function using elementary Fourier analytic methods. These Fourier series can be used to analytically continue the functions and prove the classical functional equations, which arise from the relations satisfied by the Fourier conjugate and flat Fourier series. In particular, the functional equation for the Riem...