Watson-type ₃F₂-series and summation formulae involving generalized harmonic numbers

Abstract

By applying the derivative operator to Watson-type ${}_3{F}_2$-series identities and using the bijection method of two-term difference as well as L'Hôspital rule, three families of summation formulae involving generalized harmonic numbers are established.

Keywords:

• Hypergeometric series
• Watson's ${}_3{F}_2$-series identity
• derivative operator
• Harmonic numbers

2010 Mathematics Subject Classifications:

• Primary 05A10
• Secondary 33C20

Acknowledgments

The authors are grateful to the reviewer for helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work is supported by the National Natural Science Foundations of China [grant numbers 11661032, 11301120, 11371327].