Naslov
The Feynman integral in $\mathbb R^1 \oplus \mathbb R^m$ and complex expansion of $_2F_1$

Autori
Shpot, Mykola ; Poganj, Tibor

Izvornik
Integral transforms and special functions (1065-2469) 27 (2016), 7; 533-547

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Feynman integral ; Gauss hypergeometric function ; Generalized hypergeometric function ; Appell functions ; Horn functions ; Hypergeometric transformation formulae

Sažetak
Closed form expressions are proposed for a Feynman integral over $d=D+m$ dimensional space with $(\bm x, \bm y), \, (\bm p, \bm q) \in \mathbb R^D \oplus \mathbb R^m$, 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. Several interesting relations are derived between the real and imaginary parts of $_2F_1$ and the function $H_4$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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