• DOI:10.1007/978-3-030-80219-6_9
• Corpus ID: 229923682

Hypergeometric Functions and Feynman Diagrams

@article{Kalmykov2021HypergeometricFA,
  title={Hypergeometric Functions and Feynman Diagrams},
  author={Mikhail Yu. Kalmykov and Vladimir V. Bytev and Bernd A. Kniehl and S. Moch and Bennie F. L. Ward and Scott A. Yost},
  journal={Texts \& Monographs in Symbolic Computation},
  year={2021}
}

• M. Kalmykov, V. Bytev, +3 authors S. Yost
• Published 28 December 2020
• Mathematics
• Texts & Monographs in Symbolic Computation

The relationship between Feynman diagrams and hypergeometric functions is discussed. Special attention is devoted to existing techniques for the constructionof the Y-expansion. As an example, we present a detailed discussion of the construction of the Y-expansion of the Appell function 3 around rational values of parameters via an iterative solution of differential equations. Another interesting example is the Puiseux-type solution involving a differential operator generated by a hypergeometric function of three variables. The holonomic properties of the # hypergeometric functions are briefly discussed. Mikhail Kalmykov JINR, Dubna, Russia, e-mail: [e-mail] Vladimir Bytev BLTP JINR, 141980 Dubna, Moscow region, Russia e-mail: [e-mail] Bernd A. Kniehl, II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany e-mail: [e-mail] Sven-Olaf Moch II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany e-mail: [e-mail] B.F.L. Ward Department of Physics, Baylor University, One Bear Place, # 97316, Waco, TX 76798-7316, USA email: BFL{\protect\relax$\@@underline{\hbox{\}}\mathsurround\z@$\relax}[e-mail] S.A. Yost Department of Physics, The Citadel, 171 Moultrie St., Charleston, SC 29409, USA e-mail: [e-mail]