East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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SOME INTEGRAL REPRESENTATIONS OF THE CLAUSEN FUNCTION Cl2(x) AND THE CATALAN CONSTANT G

  • Received : 2015.05.16
  • Accepted : 2016.01.14
  • Published : 2016.01.30
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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.

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References

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  2. Series representations for the Apery constant $$\zeta (3)$$ ζ ( 3 ) involving the values $$\zeta (2n)$$ ζ ( 2 n ) pp.1572-9303, 2019, https://doi.org/10.1007/s11139-018-0081-0