Vol. 35 (2025)
Articles

Two closed-form evaluations for the generalizedhypergeometric function  \({}_{4}F_{3}\left(\frac{1}{16}\right)\)

Arjun K. Rathie
Vedant College of Engineering and Technology, Rajasthan Technical University, Tulsi, Bundi District, India.
Mykola A. Shpot
Institute for Condensed Matter Physics, 79011 Lviv, Ukraine

Publicado 2024-06-11

Palabras clave

  • Generalized hypergeometric functions,
  • Ramanujan-type summation formulas,
  • Clausen function

Resumen

The objective of this short note is to provide two closed-form evaluations for the generalized hypergeometric function   \({}_4F_3\) of the argument \(\frac{1}{16}\) This is achieved by means of separating a generalized hypergeometric function \({}_3F_2\) into even and odd components, together with the use of two known results for \({}_3F_2(\pm\frac{1}{4})\) available in the literature. As an application, we obtain an interesting infinite-sum representation for the number \(\pi^2\) Certain connections with the work of Ramanujan and other authors are discussed, involving other special functions and binomial sums of different kinds.

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