A class of definite integrals involving cyclotomic polynomials and nested logarithms is considered. The results are given in terms of derivatives of the Hurwitz Zeta function. Some special cases for which such derivatives can be expressed in closed form are also considered. The integration procedure is implemented in Mathematica Version 3.1
A family of generalized definite logarithmic integrals given by $$ \int_{0}^{1}\frac{\left(x^{ i m} ...
It is shown in this paper, by making use of contour integration and the Cauchy integral theorem, tha...
The functional equation for the Hurwitz Zeta function ζ(s,a) is used to obtain formulas for derivati...
In this manuscript, the authors derive closed formula for definite integrals of combinations of powe...
AbstractThe authors present a systematic investigation of the following log-gamma integral: ∫0zlogΓ(...
The object of this paper is to derive a double integral in terms of the Hurwitz–Lerch zeta function....
This is a collection of definite integrals involving the logarithmic and polynomial functions in ter...
A class of definite integrals involving a quotient function with a reducible polynomial, logarithm a...
summary:Integrals of logarithmic and hypergeometric functions are intrinsically connected with Euler...
We provide an explicit analytical representation for a number of logarithmic integrals in terms of t...
Integrals of logarithmic and hypergeometric functions are intrinsically connected with Euler sums. I...
AbstractIt is shown that an integral representation for the extension of a general Hurwitz–Lerch zet...
This paper discusses generalizations of logarithmic and hyperbolic integrals. A new proof for an int...
We show that integrals involving the log-tangent function, with respect to any square-integrable fun...
We propose and develop yet another approach to the problem of summation of series involving the Riem...
A family of generalized definite logarithmic integrals given by $$ \int_{0}^{1}\frac{\left(x^{ i m} ...
It is shown in this paper, by making use of contour integration and the Cauchy integral theorem, tha...
The functional equation for the Hurwitz Zeta function ζ(s,a) is used to obtain formulas for derivati...
In this manuscript, the authors derive closed formula for definite integrals of combinations of powe...
AbstractThe authors present a systematic investigation of the following log-gamma integral: ∫0zlogΓ(...
The object of this paper is to derive a double integral in terms of the Hurwitz–Lerch zeta function....
This is a collection of definite integrals involving the logarithmic and polynomial functions in ter...
A class of definite integrals involving a quotient function with a reducible polynomial, logarithm a...
summary:Integrals of logarithmic and hypergeometric functions are intrinsically connected with Euler...
We provide an explicit analytical representation for a number of logarithmic integrals in terms of t...
Integrals of logarithmic and hypergeometric functions are intrinsically connected with Euler sums. I...
AbstractIt is shown that an integral representation for the extension of a general Hurwitz–Lerch zet...
This paper discusses generalizations of logarithmic and hyperbolic integrals. A new proof for an int...
We show that integrals involving the log-tangent function, with respect to any square-integrable fun...
We propose and develop yet another approach to the problem of summation of series involving the Riem...
A family of generalized definite logarithmic integrals given by $$ \int_{0}^{1}\frac{\left(x^{ i m} ...
It is shown in this paper, by making use of contour integration and the Cauchy integral theorem, tha...
The functional equation for the Hurwitz Zeta function ζ(s,a) is used to obtain formulas for derivati...
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