Quadratic Transformations of Hypergeometric Function and Series with Harmonic Numbers

In this brief note, we show how to apply Kummer’s and other quadratic transformation formulas for Gauss’ and generalized hypergeometric functions in order to obtain transformation and summation formulas for series with harmonic numbers that contain one or two continuous parameters. We also give a generating function of the sequence $\frac{(a{)}_n(1-a{)}_n}{(n!{)}^2}{H}_n$ as a combination of Gauss hypergeometric function and elementary functions.