SOME INTEGRAL REPRESENTATIONS OF THE CLAUSEN FUNCTION Cl2(x) AND THE CATALAN CONSTANT G

Choi, Junesang

• Accepted : 2016.01.14
• Published : 2016.01.30
• 24 11

Abstract

The Clausen function $Cl_2$(x) arises in several applications. A large number of indefinite integrals of logarithmic or trigonometric functions can be expressed in closed form in terms of $Cl_2$(x). Very recently, Choi and Srivatava [3] and Choi [1] investigated certain integral formulas associated with $Cl_2$(x). In this sequel, we present an interesting new definite integral formula for the Clausen function $Cl_2$(x) by using a known relationship between the Clausen function $Cl_2$(x) and the generalized Zeta function ${\zeta}$(s, a). Also an interesting integral representation for the Catalan constant G is considered as one of two special cases of our main result.

Keywords

Clausen function $Cl_2$(x);Catalan constant;Generalized zeta function

References

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