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log-sine integrals (16) 16
mathematics (11) 11
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riemann zeta function (8) 8
sums (6) 6
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integral representations (3) 3
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number theory (3) 3
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values (3) 3
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Journal of Computational and Applied Mathematics, ISSN 0377-0427, 02/2019, Volume 347, pp. 330 - 342
In this paper, we investigate the integral of xnlogp(sin(x)) for natural numbers n and p. In doing so, we recover some well-known results and remark on some... 
Riemann zeta function | Bell polynomial | Binomial coefficients | Combinatorics | Harmonic numbers | Log-sine integral | MATHEMATICS, APPLIED | Mathematics - Number Theory
Journal Article
by Mezo, I
ACTA MATHEMATICA HUNGARICA, ISSN 0236-5294, 02/2020, Volume 160, Issue 1, pp. 45 - 57
The log-sine-polylog integrals were introduced by J. M. Borwein and A. Straub during their studies on special values of the log-sine integrals. In this paper... 
SERIES | Clausen function | EPSILON-EXPANSION | MULTIPLE | alternating Euler sum | 2-LOOP | MATHEMATICS | the multiple zeta value data mine | Borwein-Straub algorithm | log-sine-polylog integral | Euler sum | multiple zeta value | log-sine integral | VALUES | polylogarihm
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 5/2018, Volume 46, Issue 1, pp. 161 - 171
In this paper, we study the sequences $$\begin{aligned} I_n=\int _0^1\mathrm {Li}_n(\sin \pi x)\mathrm {d}x\quad \text{ and }\quad J_n=\int _0^1\mathrm... 
33B15 | Polylogarithm functions | Fourier Analysis | Functions of a Complex Variable | Field Theory and Polynomials | Log-sine integrals | Hypergeometric function | Mathematics | Number Theory | Combinatorics | Gamma function | MATHEMATICS | HURWITZ ZETA-FUNCTION | Information science
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2011, Volume 363, Issue 3, pp. 1463 - 1485
We introduce certain integrals of a product of the Bernoulli polynomials and logarithms of Milnor's multiple sine functions. It is shown that all the integrals... 
Integers | Mathematical integrals | Sine function | Log integral function | Mathematical functions | Polynomials | Mathematical relations | Logarithms | Number theory | Multiple sine function | Mordell-Tornheim zeta value | Clausen function | Multiple zeta value | Log sine integral | MATHEMATICS | multiple zeta value | multiple sine function | FUNCTIONAL RELATIONS | SUMS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 01/2004, Volume 147, Issue 3, pp. 645 - 667
In this paper we analysed some series involving ( ) k and ( ) k and some other related series and derived the integral representations of those series... 
Integral representations | Catalan constant | Polylogarithms | Log-sine integrals | Riemann zeta function | Special functions
Journal Article
Integral Transforms and Special Functions, ISSN 1065-2469, 10/2011, Volume 22, Issue 10, pp. 767 - 783
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2004, Volume 147, Issue 3, pp. 645 - 667
In this paper we analysed some series involving 2k k −1k −n and 2k k −2k −n and some other related series and derived the integral representations of those... 
Log-sine integrals | Riemann zeta function | Special functions | Integral representations | Catalan constant | Polylogarithms
Journal Article
Journal of Approximation Theory, ISSN 0021-9045, 05/2015, Volume 193, pp. 74 - 88
Polylogarithms appear in many diverse fields of mathematics. Herein, we investigate relations amongst the restricted class of Nielsen-type (essentially, height... 
Multiple zeta values | Log-sine integrals | Clausen functions | Multiple polylogarithms | MATHEMATICS | VALUES | 3-LOOP FEYNMAN DIAGRAMS
Journal Article
Journal of Number Theory, ISSN 0022-314X, 05/2015, Volume 150, pp. 98 - 119
In this article, we present a variety of evaluations of series of polylogarithmic nature. More precisely, we express the special values at positive integers of... 
Harmonic sums | Binomial transformations | Mellin transforms | Bell polynomials | Polylogarithms | Log-sine integrals | Zeta values | MATHEMATICS | Poly logarithms | SUMS | Mathematics | Number Theory
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2015, Volume 143, Issue 9, pp. 3743 - 3752
of the Riemann zeta function is rich enough to capture real numbers in an approximation aspect. Precisely, we prove that any real number can be strongly... 
Riemann zeta function | Approximation property | Special values | Even values | Odd values | approximation property | MATHEMATICS, APPLIED | SERIES | REPRESENTATIONS | APPROXIMATION | odd values | even values | LOG-SINE INTEGRALS | MATHEMATICS | RAMANUJAN | SPIRIT | special values
Journal Article
Journal of the Australian Mathematical Society, ISSN 1446-7887, 02/2012, Volume 92, Issue 1, pp. 15 - 36
We provide evaluations of several recently studied higher and multiple Mahler measures using log-sine integrals. This is complemented with an analysis of... 
Clausen functions | Mahler measure | log-sine integrals | multiple polylogarithms | multiple zeta values | INTEGRALS | MATHEMATICS | EPSILON-EXPANSION | VALUES | 2-LOOP | SUMS
Journal Article
Computer Physics Communications, ISSN 0010-4655, 10/2005, Volume 172, Issue 1, pp. 45 - 59
Generalized log-sine functions Lsj(k)(θ) appear in higher order ε-expansion of different Feynman diagrams. We present an algorithm for the numerical evaluation... 
Feynman integrals | Polylogarithms | Generalized log-sine functions | SERIES | EPSILON-EXPANSION | SCALE DIAGRAMS | PHYSICS, MATHEMATICAL | 2-LOOP | INTEGRALS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | FEYNMAN DIAGRAMS | polylogarithms | POLE-MASS | FORMULAS | generalized log-sine functions | RENORMALIZATION
Journal Article
Proceedings of the 36th international symposium on symbolic and algebraic computation, 06/2011, pp. 43 - 50
We study generalized log-sine integrals at special values. At π and multiples thereof explicit evaluations are obtained in terms of Nielsen polylogarithms at... 
log-sine integrals | clausen functions | multiple polylogarithms | multiple zeta values
Conference Proceeding
Integral Transforms and Special Functions, ISSN 1065-2469, 01/2008, Volume 19, Issue 1, pp. 65 - 79
Journal Article
Integers, ISSN 1867-0652, 12/2012, Volume 12, Issue 6, pp. 1179 - 1212
We continue the analysis of higher and multiple Mahler measures using log-sine integrals as started in “Log-sine evaluations of Mahler measures” and “Special... 
Multiple Polylogarithms | Multiple Zeta Values | Log-Sine Integrals | Mahler Measure | Clausen Functions
Journal Article
Proceedings of the 2011 International Workshop on symbolic-numeric computation, 06/2012, pp. 1 - 1
The Mahler measure of a polynomial of several variables has been a subject of much study over the past thirty years. Very few closed forms are proven but many... 
Mahler measures | log-sine integral | short walks
Conference Proceeding
APPLIED MATHEMATICS AND COMPUTATION, ISSN 0096-3003, 01/2004, Volume 147, Issue 3, pp. 645 - 667
In this paper we analysed some series involving ((2k)(k))(-1) k(-n) and ((2k)(k))(-2) k(-n) and some other related series and derived the integral... 
MATHEMATICS, APPLIED | catalan constant | Riemann zeta function | integral representations | polylogarithms | log-sine integrals | special functions
Journal Article
Computer Physics Communications, ISSN 0010-4655, 2005, Volume 172, Issue 1, pp. 45 - 59
Generalized log-sine functions Ls j ( k ) ( θ ) appear in higher order ɛ-expansion of different Feynman diagrams. We present an algorithm for the numerical... 
Feynman integrals | Polylogarithms | Generalized log-sine functions | Analysis | Libraries | Algorithms
Journal Article
Experimental Mathematics, ISSN 1058-6458, 01/2001, Volume 10, Issue 1, pp. 25 - 34
We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apéry sums).... 
Clausen's function | multiple zeta values | multiple Clausen values | binomial sums | log-sine integrals | polylogarithms | Apery sums | Multiple Clausen values | Apéry sums | Polylogarithms | Log-sine integrals | Multiple zeta values | Binomial sums | MATHEMATICS | 05Axx | 11Mxx | 33Bxx | 11Bxx
Journal Article
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