• 제목/요약/키워드: Clausen function $Cl_2$(x)

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

  • Choi, Junesang
    • East Asian mathematical journal
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    • 제32권1호
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    • pp.43-46
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    • 2016
  • 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.