H.M. Srivastava, M.I. Qureshi, S.H. Malik, Some hypergeometric transformations and reduction formulas for the Gauss function and their applications involving the Clausen function
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DOI: 10.23952/jnva.5.2021.6.10
Volume 5, Issue 6, 1 December 2021, Pages 981-987
Abstract. The aim of this paper is to obtain some closed forms of hypergeometric reduction formulas for the following Gauss functions ![{}_2F_1\left[\alpha,\alpha+\frac{1}{2};2\alpha-1;z\right]](https://s0.wp.com/latex.php?latex=%7B%7D_2F_1%5Cleft%5B%5Calpha%2C%5Calpha%2B%5Cfrac%7B1%7D%7B2%7D%3B2%5Calpha-1%3Bz%5Cright%5D&bg=ffffff&fg=000000&s=0 "{}_2F_1\left[\alpha,\alpha+\frac{1}{2};2\alpha-1;z\right]")
![{_{2}F_{1}} \left[\alpha-1,\alpha-\frac{3}{2};2\alpha-1;z\right]](https://s0.wp.com/latex.php?latex=%7B_%7B2%7DF_%7B1%7D%7D+%5Cleft%5B%5Calpha-1%2C%5Calpha-%5Cfrac%7B3%7D%7B2%7D%3B2%5Calpha-1%3Bz%5Cright%5D&bg=ffffff&fg=000000&s=0 "{_{2}F_{1}} \left[\alpha-1,\alpha-\frac{3}{2};2\alpha-1;z\right]")
![{_{3}F_{2}}\left[\gamma+1,\beta,\beta+\frac{1}{2}; \gamma,2\beta;z\right]](https://s0.wp.com/latex.php?latex=%7B_%7B3%7DF_%7B2%7D%7D%5Cleft%5B%5Cgamma%2B1%2C%5Cbeta%2C%5Cbeta%2B%5Cfrac%7B1%7D%7B2%7D%3B+%5Cgamma%2C2%5Cbeta%3Bz%5Cright%5D&bg=ffffff&fg=000000&s=0 "{_{3}F_{2}}\left[\gamma+1,\beta,\beta+\frac{1}{2}; \gamma,2\beta;z\right]")
How to Cite this Article:
H.M. Srivastava, M.I. Qureshi, S.H. Malik, Some hypergeometric transformations and reduction formulas for the Gauss function and their applications involving the Clausen function, J. Nonlinear Var. Anal. 5 (2021), 981-987.