{"paper":{"title":"Feynman integral in $\\mathbb R^1\\oplus\\mathbb R^m$ and complex expansion of $_2F_1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Mykola A. 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. Several interesting relat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08876","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}