A family of shifted harmonic sums

作者：Sofo Anthony^*; Srivastava H M

来源：Ramanujan Journal, 2015, 37(1): 89-108.

DOI：10.1007/s11139-014-9600-9

• Harmonic numbers
• Riemann Zeta function
• Integral representations
• Binomial coefficients
• Euler sums
• Psi (or Digamma) function
• Polygamma functions

In this paper, we first develop a set of identities for Euler-type sums. We then investigate products of the shifted harmonic numbers and the reciprocal binomial coefficients. We briefly indicate relevant connections of the results presented here with those given by earlier authors. As by-products of our investigation, we derive several (presumably new) one-parameter and two-parameter summation formulas for the hypergeometric series at argument 1.

• 出版日期2015-5