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Let be an infinite set of linear arbitrary functionals. Also let be a certain set of basis functions such that δ i, j being (as usual) the Kronecker delta. In this paper, by defining the sequence of basis functions: in which u ( x ) is an arbitrary real function, Enlarge Image
We solve the inhomogeneous Airy differential equation and apply this result to prove that every analytic function can be approximated, on a restricted domain, by an appropriate 'Airy function' with an error bound described by a quadratic function.
In this paper, we investigate a new class of multivalent analytic functions defined by the generalized Srivastava-Attiya operator s, b . Several properties of functions belonging to this class are derived.
In this study, transformation operators, some properties of kernels and properties of spectral characteristics are studied for Sturm-Liouville operators with the Coulomb potential which have discontinuity conditions inside a finite interval.
Whilst dealing with a Schr dinger operator with a magnetic field in the complex n -space, we construct a Toeplitz operator whose Berezin symbol defines a Berezin transform for each eigenspace attached to a fixed Landau level. We give a decomposition of the action of this transform on the product...
Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erd lyi-Kober fractional integral operators. Formulas of compositions for such a generalized fractional integrals with Bessel function of the...
A new bivariate beta distribution based on the Gauss hypergeometric function is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments. The method of maximum likelihood is used to derive the...
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