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Pog\\'any","submitted_at":"2015-10-29T20:16:52Z","abstract_excerpt":"Closed form expressions are proposed for the Feynman integral\n  $$\n  I_{D, m}(p,q) = \\int\\frac{d^my}{(2\\pi)^m}\\int\\frac{d^Dx}{(2\\pi)^D}\n  \\frac1{(x-p/2)^2+(y-q/2)^4}\n  \\frac1{(x+p/2)^2+(y+q/2)^4}\n  $$ over $d=D+m$ dimensional space with $(x,y),\\,(p,q)\\in \\mathbb R^D \\oplus \\mathbb R^m$, in the special case $D=1$. We show that $I_{1,m}(p,q)$ can be expressed in different forms involving real and imaginary parts of the complex variable Gauss hypergeometric function $_2F_1$, as well as generalized hypergeometric $_2F_2$ and $_3F_2$, Horn $H_4$ and Appell $F_2$ functions. 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Shpot, Tibor K. Pog\\'any","submitted_at":"2015-10-29T20:16:52Z","abstract_excerpt":"Closed form expressions are proposed for the Feynman integral\n  $$\n  I_{D, m}(p,q) = \\int\\frac{d^my}{(2\\pi)^m}\\int\\frac{d^Dx}{(2\\pi)^D}\n  \\frac1{(x-p/2)^2+(y-q/2)^4}\n  \\frac1{(x+p/2)^2+(y+q/2)^4}\n  $$ over $d=D+m$ dimensional space with $(x,y),\\,(p,q)\\in \\mathbb R^D \\oplus \\mathbb R^m$, in the special case $D=1$. We show that $I_{1,m}(p,q)$ can be expressed in different forms involving real and imaginary parts of the complex variable Gauss hypergeometric function $_2F_1$, as well as generalized hypergeometric $_2F_2$ and $_3F_2$, Horn $H_4$ and Appell $F_2$ functions. 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