Results 91 to 100 of about 821 (208)
Solution of abel‐type hypergeometric integral equation
Mathematical Modelling and Analysis, 1997 The paper is devoted to the study of the one‐dimensional integral equation involving the Gauss hypergeometric function in the kernel. The necessary and sufficient conditions for the solvability of such an equation in the space of summable functions are ...
A. A. Kilbas +3 more
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DARBOUX EVALUATIONS OF ALGEBRAIC GAUSS HYPERGEOMETRIC FUNCTIONS
Kyushu Journal of Mathematics, 2013 This paper presents explicit expressions for algebraic Gauss hypergeometric functions. We consider solutions of hypergeometric equations with the tetrahedral, octahedral and icosahedral monodromy groups. Conceptually, we pull-back such a hypergeometric equation onto its Darboux curve so that the pull-backed equation has a cyclic monodromy group ...
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, 2012 Monodromy representations on the space of solutions of the Gauss hypergeometric equation are studied by using integrals of a multivalued function. We first establish the fact that any solution of the Gauss hypergeometric equation is expressed by the ...
Mimachi, Katsuhisa +3 more
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New extension of beta, Gauss and confluent hypergeometric functions
, 2021 There are many extensions and generalizations of Gamma and Beta functions in the literature. However, a new extension of the extended Beta function B_(ζ〖, α〗_1)^(α_2;〖 m〗_1,〖 m〗_2 ) (a_1,a_2 ) was introduced and presented here because of its important ...
Muhammad Lawan KAURANGİNİ +1 more
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TRANSFORMATIONS AND INVARIANTS FOR DIHEDRAL GAUSS HYPERGEOMETRIC FUNCTIONS
Kyushu Journal of Mathematics, 2012 Hypergeometric equations with a dihedral monodromy group can be solved in terms of elementary functions. This paper gives explicit general expressions for quadratic monodromy invariants for these hypergeometric equations, using a generalization of Clausen's formula and terminating double hypergeometric sums.
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New series expansions of the Gauss hypergeometric function [PDF]
, 2013 The Gauss hypergeometric function ${}_2F_1(a,b,c;z)$ can be computed by using the power series in powers of $z, z/(z-1), 1-z, 1/z, 1/(1-z), (z-1)/z$. With these expansions ${}_2F_1(a,b,c;z)$ is not completely computable for all complex values of $z$. As
Temme, Nico +2 more
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Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions
Journal of Computational and Applied Mathematics, 2002 The author analyzes the error of the Gauss quadrature formula to compute hypergeometric and confluent hypergeometric functions based on their integral representations. The error is analyzed both in terms of the derivatives of the integrand and in terms of the derivative-free contour integral representation of the remainder term in the case of the ...
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Potential of a Spheroid with Generalized Exponential Density Distribution
Open Astronomy, 2015 The internal potential of an inhomogeneous layered spheroid with a small ellipticity and general exponential density distribution is derived in an analytical form.
Kondratyev B. P., Kireeva E. N.
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Finite sum evaluation of the Gauss hypergeometric function in an important special case
, 1979 We present explicit results expressing the Gauss hypergeometric function F ( l + 1 , m + 1 / 2 ; n + 3 / 2
John Detrich, Robert W. Conn
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A procedure for generating infinite series identities
International Journal of Mathematics and Mathematical Sciences, 2004 A procedure for generating infinite series identities makes use of the generalized method of exhaustion by analytically evaluating the inner series of the resulting double summation.
Anthony A. Ruffa
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