Gosper–type sums with reciprocals of binomial coefficients of the form (3n+ϵn)

Abstract

We evaluate, in closed forms, twelve infinite series that contain a free variable x and binomial coefficients $(\genfrac{}{}{0ex}{}{3n+ϵ}{n})$ in the denominators. Several summation formulae resembling Gosper's sum are derived as consequences.

Keywords:

• Binomial coefficient
• Gosper sums
• beta function
• integral representation
• parametric integral
• polylogarithm
• partial fraction decomposition

2020 AMS Subject Classifications:

• Primary 11B65
• Secondary 05A10
• 33B15

Disclosure statement

No potential conflict of interest was reported by the author(s).