• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.319-332
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• 2001

The main object of this paper is first to give tow contiguous analogues of a well-known hypergeometric summation formula for $_2$F$_1$(1/2). We then apply each of these analogues with a view to evaluating the sums of several classes of series in terms of Psi(or Digamma) and the Zeta functions. Relevant connections of the series identities presented here with those given elsewhere are also pointed out.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.769-780
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• 2013

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. Very recently, Choi [6] presented explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function. In the present sequel to the investigation [6], we evaluate the log-sine and log-cosine integrals involved in more complicated integrands than those in [6], by also using the Beta function.

• East Asian mathematical journal
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• v.31 no.1
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• pp.41-53
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• 2015

A large number of series and integral representations for the Stieltjes constants (or generalized Euler-Mascheroni constants) ${\gamma}_k$ and the generalized Stieltjes constants ${\gamma}_k(a)$ have been investigated. Here we aim at presenting certain integral representations for the generalized Stieltjes constants ${\gamma}_k(a)$ by choosing to use four known integral representations for the generalized zeta function ${\zeta}(s,a)$. As a by-product, our main results are easily seen to specialize to yield those corresponding integral representations for the Stieltjes constants ${\gamma}_k$. Some relevant connections of certain special cases of our results presented here with those in earlier works are also pointed out.