Generalized Extension of Watson's theorem for the series ${}_3{F}_2(1)$

Abstract

The ${}_3{F}_2$ hypergeometric function plays a very significant role in the theory of hypergeometric and generalized hypergeometric series. Despite that ${}_3{F}_2$ hypergeometric function has several applications in mathematics, also it has a lot of applications in physics and statistics. The fundamental purpose of this research paper is to find out the explicit expression of the ${}_3{F}_2$ Watson's classical summation theorem of the form: \[ _{3}F_{2}\left[ \begin{array} [c]{ccccc}% a, & b, & c & & \\ & & & ; & 1\\ \frac{1}{2}(a+b+i+1), & 2c+j & & & \end{array} \right] \] with arbitrary $i$ and $j$, where for $i=j=0$, we get the well known Watson's theorem for the series ${}_3{F}_2(1)$.

13 pages