• East Asian mathematical journal
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• v.32 no.1
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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.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.679-689
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• 2010

By developing and using certain operators like those initiated by Burchnall-Chaundy, the authors aim at investigating several decomposition formulas associated with the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function $F_{2:0;0}^{0:3;3}$ [x, y]. For this purpose, many operator identities involving inverse pairs of symbolic operators are constructed. By employing their decomposition formulas, they also present a new group of integral representations of Eulerian type for the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function $F_{2:0;0}^{0:3;3}$ [x, y], some of which include several hypergeometric functions such as $_2F_1$, $_3F_2$, an Appell function $F_3$, and the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ functions $F_{2:0;0}^{0:3;3}$ and $F_{1:0;1}^{0:2;3}$.