scientific article; zbMATH DE number 3365595

zbMath0231.33001MaRDI QIDQ5638564

E. D. Rainville

Publication date: 1971

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

Mathematics Subject Classification ID

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to special functions (33-01)

Related Items

Obtaining Voigt Functions Via Quadrature Formula for the Fractional in Time Diffusion and Wave Problem ⋮ Shifted Gegenbauer-Gauss Collocation Method for Solving Fractional Neutral Functional-Differential Equations with Proportional Delays ⋮ On some generalized Sister Celine's polynomials ⋮ On the Wright hypergeometric matrix functions and their fractional calculus ⋮ Jacobi polynomials from compatibility conditions ⋮ Three algebraic number systems based on the q-addition with applications ⋮ A note on a further extension of Gauss’s second summation theorem with an application to the extension of two well-known combinatorial identities ⋮ Unnamed Item ⋮ On the new bicomplex generalization of Hurwitz-Lerch zeta function with properties and applications ⋮ Some new Gronwall-Bellman-Bihari type integral inequality associated with \(\psi\)-Hilfer fractional derivative ⋮ Robust spectral treatment for time-fractional delay partial differential equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Two-dimensional \((p, q)\)-heat polynomials of Gould-Hopper type ⋮ Mittag-Leffler based Bessel and Tricomi functions via umbral approach ⋮ Time Periodic Doubly Connected Solutions for the 3D Quasi-Geostrophic Model ⋮ An algebraic approach to degenerate Appell polynomials and their hybrid forms via determinants ⋮ Solving the heat equation for a perturbed magnetic Laplacian on the complex plane ⋮ Korenblum constants for various weighted Fock spaces ⋮ The Bessel difference equation ⋮ Some new Hermite-Hadamard type integral inequalities for twice differentiable \(s\)-convex functions ⋮ Continuous-time Markov processes, orthogonal polynomials and Lancaster probabilities ⋮ FINDING RESULTS FOR CERTAIN RELATIVES OF THE APPELL POLYNOMIALS ⋮ Fractional Zernike functions ⋮ Some classes of special functions using Fourier transforms of some two-Variable orthogonal polynomials ⋮ A special orthogonal complement basis for holomorphic-Hermite functions and associated 1d- and 2d-fractional Fourier transforms ⋮ Unnamed Item ⋮ Fractional calculus of the extended hypergeometric function ⋮ Invariant manifolds for the thin film equation ⋮ An approximation of the distribution function of the LIML identifiability test statistic using the method of moments ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Volterra-type convolution of classical polynomials ⋮ CERTAIN INTEGRALS INVOLVING THE PRODUCT OF GAUSSIAN HYPERGEOMETRIC FUNCTION AND ALEPH FUNCTION ⋮ Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions ⋮ Certain generating functions of Hermite - Bernoulli - Legendre polynomials ⋮ Generalized hypergeometric k-functions via (k,s)-fractional calculus ⋮ Six unified results for reducibility of the Srivastava's triple hypergeometric series H_A ⋮ Generalized Srivastava's triple hypergeometric functions and their associated properties ⋮ An Introduction to Special Functions with Some Applications to Quantum Mechanics ⋮ q-analogues of general reduction formulas by Buschman and Srivastava and an important q-operator reminding of MacRobert ⋮ Unnamed Item ⋮ Optimal logarithmic energy points on the unit sphere ⋮ Lie group—theorietic origins of certain generating functions of the generalized hypergeometric polynomials ⋮ Hook length property of \(d\)-complete posets via \(q\)-integrals ⋮ Isotropic evolution of a JBD anisotropic Bianchi universe ⋮ On multiple sums of special functions ⋮ On Gauss-Type Quadrature Rules ⋮ L^p-bounded operators involving generalized hypergeometric functions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On a Family of Hypergeometric Sobolev Orthogonal Polynomials on the Unit Circle ⋮ On the summation of Schlömilch's series ⋮ Laguerre wavelet transforms ⋮ FACTORS OF SUMS AND ALTERNATING SUMS INVOLVING BINOMIAL COEFFICIENTS AND POWERS OF INTEGERS ⋮ Higher order derivatives of R-Jacobi polynomials ⋮ Biorthogonal wavelets in a generalized Sobolev space ⋮ On the summation of series over a product of Bessel functions ⋮ A generalization of a formula due to Kummer^† ⋮ Unnamed Item ⋮ THE BRENKE TYPE GENERATING FUNCTIONS AND EXPLICIT FORMS OF MRM-TRIPLES BY MEANS OF Q-HYPERGEOMETRIC SERIES ⋮ Analytical formulae for extended $_{3}F_{2}$-series of Watson–Whipple–Dixon with two extra integer parameters ⋮ Accelerating Dougall’s $_5F_4$-sum and infinite series involving $\pi $ ⋮ On the Approximate Solutions of Singular Integral Equations Using Galerkin-Type and Collocation Methods ⋮ DD-Finite Functions Implemented in Sage ⋮ Certain results of hybrid families of special polynomials associated with appell sequences ⋮ A note on estimation in lognormal linear models ⋮ A new class of mixed Bessel functions via integral transforms ⋮ Generalized Hermite-Hadamard-type integral inequalities for \(h\)-Godunova-Levin functions ⋮ Error control of rational approximations to the exponential function ⋮ Certain properties of the Laguerre-Sheffer polynomials ⋮ Partial sums of certain classes of meromorphic functions related to the Hurwitz-Lerch zeta function ⋮ Gould-Hopper matrix-Bessel and Gould-Hopper matrix-Tricomi functions and related integral representations ⋮ Finding discrete Bessel and Tricomi convolutions of certain special polynomials ⋮ Properties of certain new special polynomials associated with Sheffer sequences ⋮ Binomial identities -- combinatorial and algorithmic aspects ⋮ Maclaurin's type infinite products involving certain transcendental functions ⋮ A unified family of multivariable Legendre poly-Genocchi polynomials ⋮ Explicit representations of biorthogonal polynomials ⋮ Infinite series formulae related to Gauss and Bailey \(_2F_1(\frac{1}{2})\)-sums ⋮ On certain hypergeometric identities deducible by using the beta integral method ⋮ Some results for \(q\)-functions of many variables ⋮ Galerkin operational approach for multi-dimensions fractional differential equations ⋮ A note on degenerate generalized Laguerre polynomials and Lah numbers ⋮ The theory of the umbral calculus. III ⋮ Christoffel-Darboux-type formulae and a recurrence for biorthogonal polynomials ⋮ Limit relations between generalized orthogonal polynomials ⋮ On the incomplete hypergeometric matrix functions ⋮ A linear algebra approach to the hybrid Sheffer-Appell polynomials ⋮ An extension of beta function, its statistical distribution, and associated fractional operator ⋮ Fractional calculus and applications of family of extended generalized Gauss hypergeometric functions ⋮ Dynamical significance of generalized fractional integral inequalities via convexity ⋮ Another look at Zagier's formula for multiple zeta values involving Hoffman elements ⋮ A unified elliptic-type integral and associated recurrence relations ⋮ Extended Mittag-Leffler function and associated fractional calculus operators ⋮ A determinantal approach to Sheffer-Appell polynomials via monomiality principle ⋮ A computable extension for D-finite functions: DD-finite functions ⋮ \(q\)-Taylor theorems, polynomial expansions, and interpolation of entire functions. ⋮ M. Jackson's bilateral \(_{3} H _{3}\)-series and extension with integer parameters ⋮ Note on the degenerate gamma function ⋮ Two-step numerical methods for parabolic differential equations ⋮ Determinantal approach to certain mixed special polynomials related to Gould-Hopper polynomials ⋮ Mean ergodic theorems for bi-continuous semigroups ⋮ On Lipschitz continuity of solutions of hyperbolic Poisson's equation ⋮ Long-time asymptotics for the porous medium equation: the spectrum of the linearized operator ⋮ Division problem of moment functionals. ⋮ Partial theta function expansions ⋮ On the solutions of certain fractional kinetic equations involving \(k\)-Mittag-Leffler function ⋮ Direct proofs of the fundamental theorem of calculus for the omega integral ⋮ Generalization of a quadratic transformation formula due to Gauss ⋮ Lancaster bivariate probability distributions with Poisson, negative binomial and gamma margins ⋮ Further results on a function relevant for conformal blocks ⋮ The theory of the umbral calculus. I ⋮ On transformations and zeros of polynomials ⋮ Analytical properties of Touchard-based hybrid polynomials via operational techniques ⋮ On a new family related to truncated exponential and Sheffer polynomials ⋮ Generalized Humbert polynomials via generalized Fibonacci polynomials ⋮ \(q\)-Tricomi functions and quantum algebra representations ⋮ Appell systems on Lie groups ⋮ A survey on Markov's theorem on zeros of orthogonal polynomials ⋮ Fractional operators associated with the \(\underline{p}\)-extended Mathieu series by using Laplace transform ⋮ Beta operator with Caputo Marichev-Saigo-Maeda fractional differential operator of extended Mittag-Leffler function ⋮ Jacobi collocation scheme for variable-order fractional reaction-subdiffusion equation ⋮ Some families of generating functions and associated hypergeometric transformation and reduction formulas ⋮ Polydispersity and optimal relaxation in the hard sphere fluid ⋮ Some new formulas involving \(\Gamma_q\) functions ⋮ On degenerate Apostol-type polynomials and applications ⋮ Geometry of Schrödinger space-times. II: Particle and field probes of the causal structure ⋮ Differentiability of bizonal positive definite kernels on complex spheres ⋮ Some properties of Legendre-Gould Hopper polynomials and operational methods ⋮ The generalized hypergeometric difference equation ⋮ Factorization of the Green's operator in the Dirichlet problem for \((-1)^m(d/dt)^{2m}\) ⋮ On a novel class of polyanalytic Hermite polynomials ⋮ Rosette harmonic mappings ⋮ A new extension of Srivastava's triple hypergeometric functions and their associated properties ⋮ On some classical type Sobolev orthogonal polynomials ⋮ A matrix recurrence for systems of Clifford algebra-valued orthogonal polynomials ⋮ Laplace operator with Caputo-type Marichev-Saigo-Maeda fractional differential operator of extended Mittag-Leffler function ⋮ Lie-theoretic generating relations involving multi-variable Bessel functions of two indices ⋮ On several unified reduction formulas for the Humbert function \(\Phi_2\) with applications ⋮ Lah numbers, Laguerre polynomials of order negative one, and the \(n\)th derivative of \(\exp(1/x)\) ⋮ Construction of some hybrid relatives of Laguerre-Appell polynomials associated with Gould-Hopper matrix polynomials ⋮ A determinantal approach to Sheffer sequences ⋮ New algorithms for approximation of Bessel transforms with high frequency parameter ⋮ Properties and graphical representations of the 2-variable form of the Simsek polynomials ⋮ Certain transformation and reduction formulas for hypergeometric series in several variables ⋮ Discriminants and functions of the second kind of orthogonal polynomials ⋮ Linear combinations of gammaoperators in \(L_p\) -- spaces ⋮ DD-finite functions in Sage ⋮ Degenerate binomial coefficients and degenerate hypergeometric functions ⋮ The method of differentiating under the integral sign ⋮ Some structural results on \(\mathrm{D}^n\)-finite functions ⋮ Operational rules and generalized special polynomials ⋮ Some fractional differential equations involving generalized hypergeometric functions ⋮ A new class of generalized Laguerre-Euler polynomials ⋮ Some inequalities involving two generalized beta functions in \(n\) variables ⋮ Several characterizations of Bessel functions and their applications ⋮ The Hilbert \(L\)-matrix ⋮ On the orthogonality of partial sums of generalized hypergeometric series ⋮ Minimum variance unbiased estimation in the Pareto distribution ⋮ Weighted Hölder continuity of hyperbolic harmonic Bloch functions. ⋮ Geometric properties of certain classes of analytic functions associated with a \(q\)-integral operator ⋮ Stokes flow with slip and Kuwabara boundary conditions. ⋮ A note on triple hypergeometric series \(H_B\) and \(H_C\) ⋮ A-acceptability of derivatives of rational approximations to EXP(Z) ⋮ Certain results on a hybrid class of the Boas-Buck polynomials ⋮ Certain new results involving multivariable aleph \((\aleph)\)-function, Srivastava polynomials, hypergeometric functions and \(\overline{H}\)-function