On the evaluation of the Appell $F_2$ double hypergeometric function
| Autor: | B. Ananthanarayan, Souvik Bera, S. Friot, O. Marichev, Tanay Pathak |
|---|---|
| Přispěvatelé: | Laboratoire de Physique des 2 Infinis Irène Joliot-Curie (IJCLab), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Institut de Physique des 2 Infinis de Lyon (IP2I Lyon), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
High Energy Physics - Theory
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] transformation [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] General Physics and Astronomy FOS: Physical sciences Mathematical Physics (math-ph) High Energy Physics - Phenomenology High Energy Physics - Phenomenology (hep-ph) High Energy Physics - Theory (hep-th) linear Hardware and Architecture Mathematics - Classical Analysis and ODEs [PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph] Classical Analysis and ODEs (math.CA) FOS: Mathematics Mathematical Physics |
| Popis: | The transformation theory of the Appell $F_2(a,b_1,b_2;c_1,c_2;x,y)$ double hypergeometric function is used to obtain a set of series representations of $F_2$ which provide an efficient way to evaluate $F_2$ for real values of its arguments $x$ and $y$ and generic complex values of its parameters $a,b_1, b_2, c_1$ and $c_2$ (i.e. in the nonlogarithmic case). This study rests on a classical approach where the usual double series representation of $F_2$ and other double hypergeometric series that appear in the intermediate steps of the calculations are written as infinite sums of one variable hypergeometric series, such as the Gauss $_2F_1$ or the $_3F_2$, various linear transformations of the latter being then applied to derive known and new formulas. Using the three well-known Euler transformations of $F_2$ on these results allows us to obtain a total of 44 series which form the basis of the Mathematica package AppellF2, dedicated to the evaluation of $F_2$. A brief description of the package and of the numerical analysis that we have performed to test it are also presented. Comment: 28 pages, 14 figures |
| Databáze: | OpenAIRE |
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