Results 51 to 60 of about 12,473 (234)
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
core +2 more sources
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
DEGENERATE GAUSS HYPERGEOMETRIC FUNCTIONS
Kyushu Journal of Mathematics, 2007 22 ...
openaire +3 more sources
Extended Riemann-Liouville type fractional derivative operator with applications
Open Mathematics, 2017 The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind.
Agarwal P., Nieto Juan J., Luo M.-J.
doaj +1 more source
Gauss’ Hypergeometric Function [PDF]
, 2007 We give a basic introduction to the properties of Gauss’ hypergeometric functions, with an emphasis on the determination of the monodromy group of the Gaussian hypergeometric equation.
openaire +1 more source
Properties of Gauss Hypergeometric function, 2F1, of special parameters
, 2023 Hyunseong Kim
+4 more sources
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
doaj +1 more source
Hypergeometric motives from Euler integral representations
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We revisit certain one‐parameter families of affine covers arising naturally from Euler's integral representation of hypergeometric functions. We introduce a partial compactification of this family. We show that the zeta function of the fibers in the family can be written as an explicit product of L$L$‐series attached to nondegenerate ...
Tyler L. Kelly, John Voight
wiley +1 more source
Study of (p, q)‐Symmetric Starlike Functions of Order η
Journal of Function Spaces, Volume 2026, Issue 1, 2026.In the field of geometric function theory, we use the (p, q)‐differential operator in the complex unit disk to describe a novel class Sp,q∗∗η of symmetrical starlike functions of order η. Several interesting properties of functions belonging to the class Sp,q∗∗η are examined, such as growth, distortion, and convolution characteristics.
Imran Khan +4 more
wiley +1 more source
New Extension of Beta Function and Its Applications
International Journal of Mathematics and Mathematical Sciences, 2018 In the present paper, new type of extension of classical beta function is introduced and its convergence is proved. Further it is used to introduce the extension of Gauss hypergeometric function and confluent hypergeometric functions. Then we study their
Mehar Chand, Hanaa Hachimi, Rekha Rani
doaj +1 more source