Abstract
The chapter reviews two theorems—one on the calculation of the higher order Bernoulli numbers and the other deals with closed-form summations of several trigonometric series. The chapter introduces known mathematical constants associated with the Gamma and multiple gamma functions such as Euler–Mascheroni Constant γ and the Log-Sine integrals, which has applications in a range of mathematic and physical problems. The gamma and the polygamma functions are used in pure and applied mathematics as well as to treat convolutions of the Rayleigh functions and to evaluate a class of log-sine integrals in an algorithmic way.
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