Geodesic
On differential equations for the Feynman integral of a~one-loop diagram
Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 3, pp. 380-387

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The Feynman integral $I(s,t)$ for one-loop diagram with four vertices is considered. With the aid of the Griffiths' method of differentiating rational differential forms with respect to the parameter, it is proved that $I(s,t)$ satisfies the system of two first order differential equations. From this system a hyperbolic partial differential equation for $I(s,t)$ is obtained, the main coefiicient of which vanishes on the Landau's manifold of the Feynman integral. 
@article{TMF_1971_9_3_a7,
     author = {V. A. Golubeva},
     title = {On differential equations for the {Feynman} integral of a~one-loop diagram},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {380--387},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a7/}
}
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V. A. Golubeva. On differential equations for the Feynman integral of a~one-loop diagram. Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 3, pp. 380-387. http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a7/