EVALUATION OF SOME SIMPLE EULER-TYPE SERIES

Khristo N. Boyadzhiev (USA)

Received January 25, 2008

References:

[1] Khristo N. Boyadzhiev, Evaluation of Euler-Zagier sums, Int. J. Math. Math. Sci. 27(7) (2001), 407-412. [2] Khristo N. Boyadzhiev, Consecutive evaluation of Euler sums, Int. J. Math. Math. Sci. 29(9) (2002), 555-561. [3] Donal F. Connon, Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers, Volume III, October 2007, arXiv:0710.4025v1. [4] Ronald L. Graham, Donald E. Knuth and Oren Patashnik, Concrete Mathematics, Addison-Wesley Publ. Co., New York, 1994. [5] Charles Jordan, Calculus of Finite Differences, Chelsea Publishing Company, New York, 1950, First ed., Budapest, 1939. [6] Anatoly P. Prudnikov, Yuri A. Brychkov and Oleg I. Marichev, Integrals and Series, Vol. 1: Elementary Functions, Gordon and Breach, 1986. [7] H. M. Srivastava and Junesang Choi, Series Associated with Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2001.

Keywords and phrases: harmonic numbers, Stirling numbers, zeta function, polylogarithms, Euler’s Beta function.