Poisson kernel and multilinear generating functions of some orthogonal polynomials

Aman Verma, V. K. Jain

Type: Article

Publication Date: 1990-03-01

Citations: 19

DOI: https://doi.org/10.1016/0022-247x(90)90306-z

View Publication

Locations

Journal of Mathematical Analysis and Applications - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Poisson kernel for the associated continuous $q$-ultraspherical polynomials	1997	Mizan Rahman Q. M. Tariq
+	SOME FAMILIES OF GENERATING FUNCTIONS FOR THE q-KONHAUSER POLYNOMIALS	2008	H. M. Srivástava Fatma Tas ̧delen Burak S ̧ ekeroˇglu
+ PDF Chat	SOME FAMILIES OF GENERATING FUNCTIONS FOR THE q-KONHAUSER POLYNOMIALS	2008	H. M. Srivástava Fatma Taşdelen Burak Şekeroǧlu
+	Around Poisson--Mehler summation formula	2011	Paweł J. Szabłowski
+	Some multilinear generating functions	1984	H. M. Srivastava
+	GENERATING FUNCTION METHOD FOR ORTHOGONAL POLYNOMIALS AND JACOBI-SZEGÖ PARAMETERS	2005	Nobuhiro Asai Izumi Kubo Hui-Hsiung Kuo
+	Generating functions and a family of special orthogonal polynomials	2017	M. Sghaier A. Khlifi
+	BILINEAR GENERATING FUNCTIONS FOR ORTHOGONAL POLYNOMIALS RELATED TO ULTRASPHERICAL POLYNOMIALS	2015	Saqib Hussain
+	Classical and Quantum Orthogonal Polynomials in One Variable	2005	Mourad E. H. Ismail
+	Generating Functions for the Ultraspherical Polynomials by Truesdell Method	2015	Tadikonda Srinivasulu V. S. Bhagavan
+	Bivariate Knop–Sahi and Macdonald polynomials related to q-ultraspherical functions	2000	Jennifer Morse
+	Some Families of Multilinear q-Generating Functions and Combinatorial q-Series Identities	1995	V. K. Jain H. M. Srivastava
+	On the structure and probabilistic interpretation of Askey–Wilson densities and polynomials with complex parameters	2011	Paweł J. Szabłowski
+	MULTILINEAR GENERATING FUNCTIONS FOR JACOBI POLYNOMIALS AND FOR THEIR TWO-VARIABLE GENERALIZATIONS	2015	N. K THAKARE H. C. MADHEKAR
+ PDF Chat	Some formulas involvingq-Jacobi and related polynomials	1990	H. M. Srivastava V. K. Jain
+	Ultraspherical (Gegenbauer) polynomials	2024	Lukong Cornelius Fai
+ PDF Chat	Multi-indexed Orthogonal Polynomials of a Discrete Variable and Exactly Solvable Birth and Death Processes	2025	Satoru Odake
+ PDF Chat	ON SUMMABLE, POSITIVE POISSON–MEHLER KERNELS BUILT OF AL-SALAM–CHIHARA AND RELATED POLYNOMIALS	2012	Paweł J. Szabłowski
+	Generating functions for certain q-orthogonal polynomials	1972	L. Carlitz
+	Around Poisson-Mehler summation formula	2016	Paweł J. Szabłowski

Works That Cite This (19)

Action	Title	Year	Authors
+	Homogeneous $$q$$ q -difference equations and generating functions for $$q$$ q -hypergeometric polynomials	2015	Jian Cao
+	Generalizations of certain Carlitz’s trilinear and Srivastava–Agarwal type generating functions	2012	Jian Cao
+ PDF Chat	On a System of q-Partial Differential Equations with Applications to q-Series	2017	Zhiguo Liu
+	Homogeneous q-partial difference equations and some applications	2016	Jian Cao
+	q-difference equations for Askey–Wilson type integrals via q-polynomials	2017	Jian Cao Da‐Wei Niu
+	Notes on Askey–Roy integral and certain generating functions for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>q</mml:mi></mml:math>-polynomials	2013	Jian Cao
+	<i>q</i>-Difference equations for generalized homogeneous<i>q</i>-operators and certain generating functions	2013	Jian Cao
+	Bivariate generating functions for Rogers–Szegö polynomials	2010	Jian Cao
+	Two q-Operational Equations and Hahn Polynomials	2024	Jing Gu Dunkun Yang Qi Bao
+ PDF Chat	Moments for Generating Functions of Al-Salam-Carlitz Polynomials	2012	Jian Cao

Works Cited by This (19)

Action	Title	Year	Authors
+	A generalization of ultraspherical polynomials	1983	Richard Askey Mourad E. H. Ismail
+	Generating functions for certain q-orthogonal polynomials	1972	L. Carlitz
+	Some Orthogonal <i>q</i>‐Polynomials	1965	W. A. Al‐Salam L. Carlitz
+	<i>Generalized Hypergeometric Functions</i>	1967	L. J. Slater Werner C. Rheinboldt
+	SERIES OF HYPERGEOMETRIC TYPE WHICH ARE INFINITE IN BOTH DIRECTIONS	1936	W. N. Bailey
+	Rogers’ Linearization Formula for the Continuous <i>q</i>-Ultraspherical Polynomials and Quadratic Transformation Formulas	1985	George Gasper
+	On the Transformation Theory of Basic Hypergeometric Functions	1951	D. B. Sears
+ PDF Chat	<i>q</i>-beta integrals and the<i>q</i>-Hermite polynomials	1988	W. A. Al‐Salam Mourad E. H. Ismail
+	Linearization and Related Formulas for <i>q</i>-Ultraspherical Polynomials	1981	David M. Bressoud
+	Positivity of the Poisson Kernel for the Continuous <i>q</i>-Ultraspherical Polynomials	1983	George Gasper Mizan Rahman