Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x) [PDF]
, 2010 We provide generalizations of two of Euler’s classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function r+2 F r+1(x) when there are additional numeratorial and denominatorial ...
Miller, A. R., Paris, Richard B.
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Gauss hypergeometric function: reduction, ε-expansion for integer/half-integer parameters and Feynman diagrams [PDF]
, 2006 The Gauss hypergeometric functions 2 F 1 with arbitrary values of parameters are reduced to two functions with fixed values of parameters, which differ from the original ones by integers.
M. Kalmykov
semanticscholar +2 more sources
Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl-Teller-Ginocchio potential wave functions [PDF]
Computer Physics Communications, 2007 The fast computation of the Gauss hypergeometric function F 1 2 with all its parameters complex is a difficult task. Although the F 1 2 function verifies numerous analytical properties involving power series expansions whose implementation is apparently ...
N. Michel, M. Stoitsov
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Hypergeometric representation of the two-loop equal mass sunrise diagram [PDF]
, 2006 A recurrence relation between equal mass two-loop sunrise diagrams differing in dimensionality by 2 is derived and it's solution in terms of Gauss' 2F1 and Appell's F_2 hypergeometric functions is presented.
Appell +46 more
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Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z)
Kuwait Journal of Science, 2023 The role which hypergeometric functions have in the numerical and symbolic calculation, especially in the fields of applied mathematics and mathematical physics motivated research in this paper.
Gradimir V. Milovanović +2 more
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Clausen's series 3F2(1) with integral parameter differences and transformations of the hypergeometric function 2F2(x) [PDF]
, 2012 We obtain summation formulas for the hypergeometric series 3 F 2(1) with at least one pair of numeratorial and denominatorial parameters differing by a negative integer.
Miller, A. R., Paris, Richard B.
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Numerical Evaluation of the Gauss Hypergeometric Function with the hypergeo Package
The R Journal, 2015 This paper introduces the hypergeo package of R routines for numerical calculation of hypergeometric functions. The package is focussed on efficient and accurate evaluation of the Gauss hypergeometric function over the whole of the complex plane within ...
R. Hankin
semanticscholar +1 more source
Mathematics, 2022 Given real parameters a,b,c and integer shifts n1,n2,m, we consider the ratio R(z)=2F1(a+n1,b+n2;c+m;z)/2F1(a,b;c;z) of the Gauss hypergeometric functions.
Alexander Dyachenko, Dmitrii Karp
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A generalization of Clausen's identity
, 2009 The paper aims to generalize Clausen's identity to the square of any Gauss hypergeometric function. Accordingly, solutions of the related 3rd order linear differential equation are found in terms of certain bivariate series that can reduce to 3F2 series ...
G.E. Andrews +6 more
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DIHEDRAL GAUSS HYPERGEOMETRIC FUNCTIONS
Kyushu Journal of Mathematics, 2011 Gauss hypergeometric functions with a dihedral monodromy group can be expressed as elementary functions, since their hypergeometric equations can be transformed to Fuchsian equations with cyclic monodromy groups by a quadratic change of the argument variable.
openaire +3 more sources