Multi-omic human neural organoid cell atlas of the posterior brain
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Extended hypergeometric and confluent hypergeometric functions
The 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 \(
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Integral transforms and probability distributions involving a generalized hypergeometric function
Georgian Mathematical Journal, 2021Various extensions of the beta function together with their associated extended hypergeometric and confluent hypergeometric functions have been introduced and investigated.
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ON SOME EXTENDED SPECIAL FUNCTIONS WITH THE BI-FOX-WRIGHT FUNCTION KERNEL
JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES, 2023In the present article, our main goal is to study the new extended beta, Gauss and confluent hypergeometric functions defined by using the two Fox-Wright functions as their kernel.
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