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Extended hypergeometric and confluent hypergeometric functions
Applied Mathematics and Computation, 2004The functions under consideration are the extended Gaussian hypergeometric function \[ F_p(a,b;c,z)= {1\over B(b,c- b)} \int^1_0 t^{b-1}(1- t)^{c-b-1}(1- zt)^{-a}\exp\Biggl[-{p\over t(1- t)}\Biggr]\,dt \] and its confluent counterpart \(\Phi_p(b;c;z)\) with \(\exp(zt)\) in place of \((1- zt)^{-a}\). The authors discuss differentiation with respect to \(
Chaudhry, M. Aslam +3 more
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Extended Multivariable Hypergeometric Functions
2019In this chapter, we define an extension of multivariable hypergeometric functions. We obtain a generating function for these functions. Furthermore, we derive a family of multilinear and multilateral generating functions for these extended multivariable hypergeometric functions.
Erkuş-Duman, Esra, Düzgün, Düriye
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EXPANSIONS OF HYPERGEOMETRIC FUNCTIONS
The Quarterly Journal of Mathematics, 1942Not ...
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Computing the Hypergeometric Function
Journal of Computational Physics, 1997The Gauss hypergeometric function \({}_2F_1(a,b;c;x)\) is computed for real values of the variables \(a, b, c\) and \(x\). Transformation formulas are used to give a suitable \(x-\)interval for the power series. Great care is taken for the divergences that occur for certain values of \(a, b\) and \(c\) in the transformations.
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