Infinite series involving harmonic numbers of convergence rate 1/2

Abstract

By means of the ‘linearization’ method, Bailey's summation theorem for ${}_2{F}_1(\frac{1}{2})$-series is extended with integer parameters. It is then in turn utilized systematically to explore infinite series of convergence rate 1/2 involving harmonic numbers, squares of central binomial coefficients and multinomial coefficients. Numerous remarkable summation formulae are established in closed form.

Keywords:

• Harmonic number
• central binomial coefficient
• multinomial coefficient
• hypergeometric series
• linearization method

2020 AMS Subject Classifications:

• Primary 33C20
• Secondary 65B10

Disclosure statement

No potential conflict of interest was reported by the author.