Distribution of LRC for testing sphericity of a complex multivariate Gaussian model.
Eine arithmetische Eigenschaft der Koeffizienten hypergeometrischer Funktionen mit algebraischen Parametern.
Expansion formulae for the products of Meijer's G-function and Bessel functions
Expansion Of Kampé De Fériet's Function
Expansion of Kampé de Fériet's function.
Expansion theorems for the H function of several complex variables.
Exponential-Bessel partial differential equation and Fox’s -function
Extension of analytic number theory and the theory of regularized harmonic series from Dirichlet series to Bessel series.
Extension of certain classes of generating functions
Finite and infinite series involving MacRobert's E-Function
Finite monodromy of Pochhammer equation
We consider the monodromy group of the Pochhammer differential equation . Let be the reduce equation modulo a prime . Then we show that is finite if and only if has a full set of polynomial solutions for almost all primes .
Fonctions hypergéométriques en plusieurs variables et espaces des modules de variétés abéliennes
Fractional Calculus of P-transforms
MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99The fractional calculus of the P-transform or pathway transform which is a generalization of many well known integral transforms is studied. The Mellin and Laplace transforms of a P-transform are obtained. The composition formulae for the various fractional operators such as Saigo operator, Kober operator and Riemann-Liouville fractional integral and differential operators with P-transform are proved. Application of the P-transform in reaction rate...
Fractional Integration and Fractional Differentiation of the M-Series
Mathematics Subject Classification: 26A33, 33C60, 44A15In this paper a new special function called as M-series is introduced. This series is a particular case of the H-function of Inayat-Hussain. The M-series is interesting because the pFq -hypergeometric function and the Mittag-Leffler function follow as its particular cases, and these functions have recently found essential applications in solving problems in physics, biology, engineering and applied sciences. Let us note that the Mittag-Leffler ...
Fractional Integration of the Product of Bessel Functions of the First Kind
Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for the product of cosine...
Gaudin's model and the generating function of the Wroński map
We consider the Gaudin model associated to a point z ∈ ℂⁿ with pairwise distinct coordinates and to the subspace of singular vectors of a given weight in the tensor product of irreducible finite-dimensional sl₂-representations, [G]. The Bethe equations of this model provide the critical point system of a remarkable rational symmetric function. Any critical orbit determines a common eigenvector of the Gaudin hamiltonians called a Bethe vector. In [ReV], it was shown that for generic...
Generalized function fractional integration operators in some classes of analytic functions
Generalized Picard lattices arising from half-integral conditions
-function with complex parameters. I: Existence.
-function with complex parameters. II: Evaluation.