scientific article
From MaRDI portal
Publication:3319049
zbMath0535.33001MaRDI QIDQ3319049
H. L. Manocha, Hari M. Srivastava
Publication date: 1984
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
generating functionsfractional derivativesLaguerre functionshypergeometric functionsLie groupsJacobi polynomialsgamma and beta functionsLagrange's expansion
Fractional derivatives and integrals (26A33) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Multidimensional problems (41A63) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60) Research exposition (monographs, survey articles) pertaining to special functions (33-02) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Classical hypergeometric functions, ({}_2F_1) (33C05)
Related Items (only showing first 100 items - show all)
Bilateral generating functions and operational methods ⋮ Vector orthogonal polynomials with Bochner's property ⋮ On an operational matrix method based on generalized Bernoulli polynomials of level \(m\) ⋮ Some families of bilinear and bilateral generating functions ⋮ Combinatorics of second derivative: graphical proof of Glaisher-Crofton identity ⋮ Binomial identities -- combinatorial and algorithmic aspects ⋮ Properties of functions involving struve function ⋮ Convolutions of the generalized Morgan-Voyce polynomials ⋮ The Clausenian hypergeometric function \({}_3 F_2\) with unit argument and negative integral parameter differences ⋮ Some further properties of a linear operator associated with the \(\lambda\)-generalized Hurwitz-Lerch zeta function related to the class of meromorphically univalent functions ⋮ Some families of generating functions for the Jacobi polynomials ⋮ Some families of the incomplete \(H\)-functions and the incomplete \(\overline H \)-functions and associated integral transforms and operators of fractional calculus with applications ⋮ Generalized multiple integral representations for a large family of polynomials with applications ⋮ Extended Riemann-Liouville type fractional derivative operator with applications ⋮ A unified theory of polynomial expansions and their applications involving Clebsch-Gordan type linearization relations and Neumann series ⋮ Some general theorems on generating functions and their applications ⋮ Some reduction formulas for multiple hypergeometric series ⋮ A note on certain operational representations for the Laguerre polynomials ⋮ On certain Schlömilch-type series ⋮ An incomplete Lipschitz-Hankel integral of \(K_ 0\) ⋮ Generating functions for a class of \(q\)-polynomials ⋮ Generating relations and multivariable Aleph-function ⋮ Some families of generating functions for the Bessel polynomials ⋮ A class of numbers associated with the Lucas numbers ⋮ Laplace type integral expressions for a certain three-parameter family of generalized Mittag-Leffler functions with applications involving complete monotonicity ⋮ Some multilinear generating functions for q-Hermite polynomials ⋮ Computation of Jacobi functions of the second kind for use in nearside-farside scattering theory ⋮ Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Continuous case ⋮ Fourier transform representation of the generalized hypergeometric functions with applications to the confluent and Gauss hypergeometric functions ⋮ Representation of the Coulomb matrix elements by means of Appell hypergeometric function \(F_2\) ⋮ Combinatorics of Jacobi-configurations. III: The Srivastava-Singhal generating function revisited ⋮ A theorem on generating functions and its applications ⋮ \(SU(2)\) and \(SU(1,1)\) algebra eigenstates: A unified analytic approach to coherent and intelligent states ⋮ A Lipschitz-Hankel integral of \(K_ 0\) ⋮ Lie algebras of difference-differential operators and Appell functions \(F_ 1\) ⋮ Generating functions for special polynomials and numbers including Apostol-type and Humbert-type polynomials ⋮ Some families of generating functions for the Jacobi and related orthogonal polynomials ⋮ A note on boundedness properties of Wrights's generalized hypergeometric functions ⋮ Extensions of two \(q\)-series expansions with applications to biorthogonal rational functions ⋮ Linearization coefficients for Sheffer polynomial sets via lowering operators ⋮ Positive definite functions on complex spheres and their walks through dimensions ⋮ The truncated exponential polynomials, the associated Hermite forms and applications ⋮ Some families of hypergeometric generating functions associated with multiple series transformations. ⋮ On a Kummer-type transformation for the generalized hypergeometric function \(_{2}F_{2}\) ⋮ Certain classes of finite-series relationships and generating functions involving the generalized Bessel polynomials. ⋮ A unified class of analytic functions involving a generalization of the Srivastava-Attiya operator ⋮ Some results on quasi-monomiality. ⋮ On a new family of Hermite polynomials associated to parabolic cylinder functions ⋮ Operational methods, fractional operators and special polynomials. ⋮ Generalized Hermite polynomials associated with functions of parabolic cylinder ⋮ Generalized shift operators and pseudo-polynomials of fractional order. ⋮ Orthogonality of some polynomial sets via quasi-monomiality. ⋮ Some families of hypergeometric transformations and generating relations. ⋮ New class of generating functions associated with generalized hypergeometric polynomials. ⋮ Certain classes of polynomial expansions and multiplication formulas. ⋮ Some Clebsch-Gordan type linearization relations and associated families of Dirichlet integrals. ⋮ Extensions of certain classical integrals of Erdélyi for Gauss hypergeometric functions. ⋮ On multiindices and multivariables presentation of the Voigt functions. ⋮ On irreducible \(p,q\)-representations of gl(2). ⋮ Integral transforms and Chebyshev-like polynomials. ⋮ Certain classes of generating functions for the Jacobi and related hypergeometric polynomials. ⋮ Extension of certain types of generating relations ⋮ Factorial functions and Stirling numbers of fractional orders ⋮ Lie-theoretic generating relations of two variable Laguerre polynomials ⋮ An application of fractional calculus ⋮ Remarks on some associated Laguerre integral results ⋮ Integral-type generalizations of operators obtained from certain multivariate polynomials ⋮ Incomplete Weber integrals of cylindrical functions ⋮ Some further reduction formulas for certain classes of generalized multiple hypergeometric series arising in physical, astrophysical, and quantum chemical applications ⋮ A note on the multidimensional Weyl fractional operator ⋮ \(d\)-Orthogonality of Hermite type polynomials ⋮ Incomplete Lipschitz-Hankel integrals of Struve functions ⋮ Some connections between generalized Voigt functions with the different parameters ⋮ Legendre polynomials: Lie methods and monomiality ⋮ New results involving a certain class of \(q\)-orthogonal polynomials ⋮ Some generating functions for the Jacobi polynomials ⋮ On the Mehler formula for Hermite polynomials ⋮ The Lie theory of hypergeometric functions arising from \((1-\sum^ k_{i=1}z_ i)^ \lambda(1-\sum^ r_{j=k+1}z_ j)^ -\lambda\) ⋮ On linearization coefficients of Jacobi polynomials ⋮ Some families of generating functions for a class of bivariate polynomials ⋮ Monomiality and partial differential equations ⋮ A reduction formula for the Kampé de Fériet function ⋮ Fractional integral operators involving a general class of polynomials ⋮ On a multivariable extension for the extended Jacobi polynomials ⋮ Further notes on the associated alpha-functions and related integrals in the theory of the light changes of eclipsing variables ⋮ Some new generating functions for the Hermite polynomials ⋮ Some triple series and triple integral equations ⋮ Operational rules and arbitrary order Hermite generating functions ⋮ On certain generalized families of unified elliptic-type integrals pertaining to Euler integrals and generating functions ⋮ Some generating functions for the Laguerre and related polynomials ⋮ Decomposition formulas for Srivastava's hypergeometric function \(H_A\) on Saran functions ⋮ Generalized polynomials, operational identities and their applications ⋮ Incomplete Lipschitz-Hankel integrals of Anger and Weber functions ⋮ Commutativity of the Leibniz rules in fractional calculus ⋮ Operational identities and properties of ordinary and generalized special functions ⋮ Some families of generating functions associated with the Stirling numbers of the second kind ⋮ Some polynomial systems associated with a certain family of differential operators ⋮ Orthogonality relations and generating functions for the generalized Bessel polynomials ⋮ Some applications of fractional calculus operators to obtain classes of analytic and multivalent functions ⋮ Some \(q\)-generating functions associated with basic multiple hypergeometric series
This page was built for publication:
