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ON A NEW CLASS OF INTEGRALS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTION 3F2
김인숙,Shantha Kumari. K.,Yashoverdhan Vyas 호남수학회 2018 호남수학학술지 Vol.40 No.1
The main aim of this research paper is to evaluate thegeneral integral of the formZ 10xc 1(1 x)c+` [1 + x + (1 x)] 2c ` 13F2 a; b; 2c + ` + 112 (a + b + i + 1); 2c + j;(1 + )x1 + x + (1 x) dxin the most general form for any ` 2 Z; and i; j = 0; 1; 2. The re-sults are established with the help of generalized Watson's summa-tion theorem due to Lavoie, et al. Fifty interesting general integralshave also been obtained as special cases of our main ndings. The main aim of this research paper is to evaluate thegeneral integral of the formZ 10xc 1(1 x)c+` [1 + x + (1 x)] 2c ` 13F2 a; b; 2c + ` + 112 (a + b + i + 1); 2c + j;(1 + )x1 + x + (1 x) dxin the most general form for any ` 2 Z; and i; j = 0; 1; 2. The re-sults are established with the help of generalized Watson's summa-tion theorem due to Lavoie, et al. Fifty interesting general integralshave also been obtained as special cases of our main ndings.
ON A NEW CLASS OF INTEGRALS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTION <sub>3</sub>F<sub>2</sub>
( Insuk Kim ),( Shantha Kumari. K. ),( Yashoverdhan Vyas ) 호남수학회 2018 호남수학학술지 Vol.40 No.1
The main aim of this research paper is to evaluate the general integral of the form in the most general form for any ℓ□ Z; and i, j = 0, ±1, ±2. The re- sults are established with the help of generalized Watson's summa- tion theorem due to Lavoie, et al. Fifty interesting general integrals have also been obtained as special cases of our main findings.
Kilicman, Adem,Kurumujji, Shantha Kumari,Rathie, Arjun K. Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.2
In the theory of hypergeometric and generalized hypergeometric series, the well-known and very useful identity due to Bailey (which is a generalization of the Preece's identity) plays an important role. The aim of this research paper is to provide generalizations of Bailey's identity involving products of generalized hypergeometric series in the most general form. A few known, as well as new results, have also been obtained as special cases of our main findings.