[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2007.22.2.219

SOME IDENTITIES INVOLVING THE LEGENDRE'S CHI-FUNCTION

Choi, June-Sang (DEPARTMENT OF MATHEMATICS DONGGUK UNIVERSITY)

Publication Information

Communications of the Korean Mathematical Society / v.22, no.2, 2007 , pp. 219-225 More about this Journal

Abstract

Since the time of Euler, the dilogarithm and polylogarithm functions have been studied by many mathematicians who used various notations for the dilogarithm function $Li_2(z)$ . These functions are related to many other mathematical functions and have a variety of application. The main objective of this paper is to present corrected versions of two equivalent factorization formulas involving the Legendre's Chi-function $\chi_2$ and an evaluation of a class of integrals which is useful to evaluate some integrals associated with the dilogarithm function.

Keywords

dilogarithm function; polylogarithm function; Legendre's chi-function; gamma function; Riemann Zeta function; Euler-Mascheroni's constant;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)
Times Cited By SCOPUS : 1

1	V. S. Adamchik and K. S. Kolbig, A definite integral of a product of two polylogarithms, SIAM J. Math. Anal. 19 (1988), no. 4, 926-938 DOI
2	D. Bowman and D. M. Bradley, Multiple polylogarithms: A brief survey, Contemporary Math. 291 (2001), 1-21 DOI
3	J. Choi and H. M. Srivastava, Evaluation of higher-order derivatives of the Gamma function, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 11 (2000), 9-18
4	M. Jung, Y. J. Cho, and J. Choi, Euler sums evaluatable from integrals, Commun. Korean Math. Soc. 19 (2004), 545-555 과학기술학회마을 DOI
5	A. M. Legendre, The Integral Calculus, Vol. 2 Macmillan & Co., 1922
6	M. R. Spiegel and J. Liu, Mathematical Handbook of Formulas and Tables, 2nd Edi., McGraw-Hill, 1999
7	H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001
8	L. Lewin, Polylogarithms and Associated Functions, Elsevier North Holland, Inc., 1981
9	W. Spence, An Essay on The Theory of The Various Orders of Logarithmic Transcendents; with An Inquiry into Their Applications To The Integral Calculus and The Summation of Series, John Murray, 32, Fleet Street, and Archibald Constable and Company, Edinburgh, 1809