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RODRIGUES TYPE FORMULA FOR ORTHOGONAL POLYNOMIALS ON THE UNIT BALL
"... Abstract. For a class of weight functions invariant under reflection groups on the unit ball, a family of orthogonal polynomials is defined via a Rodrigues type formula using the Dunkl operators. Their properties and their relation with several other bases are explored. 1. ..."
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Abstract. For a class of weight functions invariant under reflection groups on the unit ball, a family of orthogonal polynomials is defined via a Rodrigues type formula using the Dunkl operators. Their properties and their relation with several other bases are explored. 1.
Rodriguestype formulae for Hermite and Laguerre polynomials
"... In this paper we give new proofs of some elementary properties of the Hermite and Laguerre orthogonal polynomials. We establish Rodriguestype formulae and other properties of these special functions, using suitable operators defined on the Lie algebra of endomorphisms to the vector space of infinite ..."
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In this paper we give new proofs of some elementary properties of the Hermite and Laguerre orthogonal polynomials. We establish Rodriguestype formulae and other properties of these special functions, using suitable operators defined on the Lie algebra of endomorphisms to the vector space
The Askeyscheme of hypergeometric orthogonal polynomials and its qanalogue
, 1998
"... We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a qanalogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order differenti ..."
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Cited by 577 (6 self)
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differential or difference equation, the forward and backward shift operator, the Rodriguestype formula and generating functions of all classes of orthogonal polynomials in this scheme. In chapter 2 we give the limit relations between different classes of orthogonal polynomials listed in the Askey
Rodrigues formulas for the Macdonald polynomials
, 1997
"... We present formulas of Rodrigues type giving the Macdonald polynomials for arbitrary partitions through the repeated application of creation operators B k , k = 1; : : : ; `() on the constant 1. Three expressions for the creation operators are derived one from the other. When the last of these e ..."
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Cited by 23 (2 self)
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We present formulas of Rodrigues type giving the Macdonald polynomials for arbitrary partitions through the repeated application of creation operators B k , k = 1; : : : ; `() on the constant 1. Three expressions for the creation operators are derived one from the other. When the last
A FormulaeasTypes Notion of Control
 In Conference Record of the Seventeenth Annual ACM Symposium on Principles of Programming Languages
, 1990
"... The programming language Scheme contains the control construct call/cc that allows access to the current continuation (the current control context). This, in effect, provides Scheme with firstclass labels and jumps. We show that the wellknown formulaeastypes correspondence, which relates a constr ..."
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Cited by 293 (0 self)
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constructive proof of a formula ff to a program of type ff, can be extended to a typed Idealized Scheme. What is surprising about this correspondence is that it relates classical proofs to typed programs. The existence of computationally interesting "classical programs"  programs of type ff, where
The Computational Complexity of Propositional STRIPS Planning
 Artificial Intelligence
, 1994
"... I present several computational complexity results for propositional STRIPS planning, i.e., STRIPS planning restricted to ground formulas. Different planning problems can be defined by restricting the type of formulas, placing limits on the number of pre and postconditions, by restricting negation ..."
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Cited by 363 (3 self)
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I present several computational complexity results for propositional STRIPS planning, i.e., STRIPS planning restricted to ground formulas. Different planning problems can be defined by restricting the type of formulas, placing limits on the number of pre and postconditions, by restricting negation
On the assessment of surface heat flux and evaporation using large scale parameters
 Mon. Weather Rev
, 1972
"... ABSTRACTIn an introductory review it is reemphasized that the largescale parameterization of the surface fluxes of sensible and latent heat is properly expressed in terms of energetic considerations over land while formulas of the bulk aerodynamic type are most suitable over the sea. A general fra ..."
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Cited by 355 (0 self)
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ABSTRACTIn an introductory review it is reemphasized that the largescale parameterization of the surface fluxes of sensible and latent heat is properly expressed in terms of energetic considerations over land while formulas of the bulk aerodynamic type are most suitable over the sea. A general
A logic programming language with lambdaabstraction, function variables, and simple unification
 Extensions of Logic Programming. Springer Lecture Notes in Artificial Intelligence
, 1990
"... A meta programming language must be able to represent and manipulate such syntactic structures as programs, formulas, types, and proofs. A common characteristic of all these structures is that they involve notions of abstractions, scope, bound and free variables, substitution instances, and equality ..."
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Cited by 314 (27 self)
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A meta programming language must be able to represent and manipulate such syntactic structures as programs, formulas, types, and proofs. A common characteristic of all these structures is that they involve notions of abstractions, scope, bound and free variables, substitution instances
On the Rodrigues Formula Solution of the HypergeometricType Differential Equation
"... Copyright © 2013 W. Robin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we present a new systematic approach to the ..."
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to the solution of the hypergeometriclike differential equation and its associated equation. The method produces, tout court, the general solution of these equations in the form of a combination of a standard Rodrigues formula and a ‘generalized ’ Rodrigues formula, of a type due originally to Gonçalves [5
containing the Rodrigues type polynomial
"... Abstract. In the present paper, we obtain the inverse Laplace transform involving the product of a general class of polynomials Qτ j=1 Sm j n (xj), the polynomial j set S α,β,0 µ [x], and the Hfunction of several complex variables. On account of the most general character of the general class of po ..."
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Abstract. In the present paper, we obtain the inverse Laplace transform involving the product of a general class of polynomials Qτ j=1 Sm j n (xj), the polynomial j set S α,β,0 µ [x], and the Hfunction of several complex variables. On account of the most general character of the general class of polynomials, generalized polynomial set and the Hfunction of several complex variables involved herein, the inverse Laplace transform of the product of a large number of special functions involving one or more variables, occurring frequently in the problems of theoretical physics and engineering sciences can be obtained as particular cases of our main findings. For the sake of illustration, we obtain the inverse Laplace transform of product of two generalized Hermite polynomials given by Gould and Hopper [9], and the Hfunction of several complex variables. Our result provides a unification of the inverse Laplace transform pertaining to the product of polynomials and special functions earlier obtained by Soni and Singh [14,15], Gupta and Soni [10,11], Srivastava [2], and Rathie [13]. 1.
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