Identities for the harmonic numbers and binomial coefficients

The Ramanujan Journal - Tập 25 Số 1 - Trang 93-113 - 2011
Anthony Sofo1, H. M. Srivástava2
1School of Engineering and Science, Victoria University, P.O. Box 14428, Melbourne City, Victoria, 8001, Australia
2Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada

Tóm tắt

Từ khóa


Tài liệu tham khảo

Alzer, H., Karayannakis, D., Srivastava, H.M.: Series representations of some mathematical constants. J. Math. Anal. Appl. 320, 145–162 (2006)

Basu, A.: A new method in the study of Euler sums. Ramanujan J. 16, 7–24 (2008)

Basu, A., Apostol, T.M.: A new method for investigating Euler sums. Ramanujan J. 4, 397–419 (2000)

Borwein, D., Borwein, J., Girgensohn, R.: Explicit evaluation of Euler sums. Proc. Edinb. Math. Soc. (Ser. 2) 38, 277–294 (1995)

Chen, X., Chu, W.-C.: Dixon’s 3 F 2(1)-series and identities involving harmonic numbers and the Riemann Zeta function. Discrete Math. 310, 83–94 (2010)

Choi, J., Cvijović, D.: Values of the polygamma functions at rational arguments. J. Phys. A: Math. Theor. 40, 15019–15028 (2007)

Choi, J., Srivastava, H.M.: Explicit evaluation of Euler and related sums. Ramanujan J. 10, 51–70 (2005)

Choi, J., Srivastava, H.M.: Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions, multiple Euler sums and log-sine integrals. Math. Nachr. 282, 1709–1723 (2009)

Chu, W.-C., Fu, A.M.: Dougall–Dixon formula and harmonic number identities. Ramanujan J. 18, 11–31 (2009)

Euler, L.: Opera Omnia, Ser. 1, vol. 15. Teubner, Berlin (1917)

Flajolet, P., Salvy, B.: Euler sums and contour integral representations. Exp. Math. 7, 15–35 (1998)

Kölbig, K.: The polygamma function ψ(x) for x=1/4 and x=3/4. J. Comput. Appl. Math. 75, 43–46 (1996)

Kölbig, K.: The polygamma function and the derivatives of the cotangent function for rational arguments. CERN-IT-Reports CERN-CN, pp. 96–005 (1996)

Krattenthaler, C., Rao, K.S.: Automatic generation of hypergeometric identities by the beta integral method. J. Comput. Math. Appl. 160, 159–173 (2003)

Nielsen, N.: Die Gammafunktion. Chelsea, New York (1965)

Petojević, A., Srivastava, H.M.: Computation of Euler’s type sums of the products of Bernoulli numbers. Appl. Math. Lett. 22, 796–801 (2009)

Rassias, T.M., Srivastava, H.M.: Some classes of infinite series associated with the Riemann Zeta and Polygamma functions and generalized harmonic numbers. Appl. Math. Comput. 131, 593–605 (2002)

Sofo, A.: Computational Techniques for the Summation of Series. Kluwer Academic/(Plenum), New York (2003)

Sofo, A.: Integral forms of sums associated with harmonic numbers. Appl. Math. Comput. 207, 365–372 (2009)

Sofo, A.: Sums of derivatives of binomial coefficients. Adv. Appl. Math. 42, 123–134 (2009)

Sofo, A.: Harmonic numbers and double binomial coefficients. Integral Transforms Spec. Funct. 20, 847–857 (2009)

Sondow, J., Weisstein, E.W.: Harmonic number, From MathWorld: A Wolfram Web Rescources; http://mathworld.wolfram.com/HarmonicNumber.html

Srivastava, H.M., Choi, J.: Series Associated with the Zeta and Related Functions. Kluwer Academic, Dordrecht/Boston/London (2001)

Wolfram Research Incorporated: Mathematica. Wolfram Research Incorporated, Champaign (2009)