• 호남수학학술지
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• 제40권4호
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• pp.809-816
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• 2018

The aim of this research paper is to evaluate fifty double integrals invoving generalized hypergeometric function (25 each) in the form of $${{\int}^1_0}{{\int}^1_0}\;x^{{\gamma}-1}y^{{\gamma}+c-1}(1-x)^{c-1}(1-y)^{c+{\ell}}(1-xy)^{{\delta}-2c-{\ell}-1}{\times}_3F_2\[{^{a,\;b,\;2c+{\ell}+1}_{\frac{1}{2}(a+b+i+1),\;2c+j}}\;;{\frac{(1-x)y}{1-xy}}\]dxdy$$ and $${{\int}^1_0}{{\int}^1_0}\;x^{{\gamma}-1}y^{{\gamma}+c+{\ell}}(1-x)^{c+{\ell}}(1-y)^{c-1}(1-xy)^{{\delta}-2c-{\ell}-1}{\times}_3F_2\[{^{a,\;b,\;2c+{\ell}+1}_{\frac{1}{2}(a+b+i+1),\;2c+j}}\;;{\frac{1-y}{1-xy}}\]dxdy$$ in the most general form for any ${\ell}{\in}{\mathbb{Z}}$ and i, j = 0, ${\pm}1$, ${\pm}2$. The results are derived with the help of generalization of Edwards's well known double integral due to Kim, et al. and generalized classical Watson's summation theorem obtained earlier by Lavoie, et al. More than one hundred ineteresting special cases have also been obtained.