Log-Sine and Log-Cosine Integrals

Abstract

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the logsine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. The main object of this paper is to present explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function.

Integrals of logarithmic and hypergeometric functions

“…Brought to you by | Victoria University Australia Authenticated Download Date | 7/11/17 6:14 AM Choi [3] has also given the definition, in terms of log-sine functions…”

Families of Integrals of Polylogarithmic Functions

“…Choi [27,28] has also produced many interesting examples of log-sine and log-cosine integrals. Mezo [29] continues the study and considers the class of integrals…”

Evaluation of log-tangent integrals by series involving ζ(2n+1)

“…One can also use the translation property (7) to show that Corollary 2. For any positive integer n and a given real y,…”

“…The higher moments were studied differently by several authors (see, for example , [15]). Furthermore, many families of log-sine and log-cosine integrals were evaluated explicitly by Choi and Srivastava; see [7] and [10]. In this note, we shall study integrals involving the log-tangent function for a certain class of functions f defined on the interval 0, π 2 ; namely…”