4,595 research outputs found
Generalized Burchnall-Type Identities for Orthogonal Polynomials and Expansions
Burchnall's method to invert the Feldheim-Watson linearization formula for
the Hermite polynomials is extended to all polynomial families in the
Askey-scheme and its -analogue. The resulting expansion formulas are made
explicit for several families corresponding to measures with infinite support,
including the Wilson and Askey-Wilson polynomials. An integrated version gives
the possibility to give alternate expression for orthogonal polynomials with
respect to a modified weight. This gives expansions for polynomials, such as
Hermite, Laguerre, Meixner, Charlier, Meixner-Pollaczek and big -Jacobi
polynomials and big -Laguerre polynomials. We show that one can find
expansions for the orthogonal polynomials corresponding to the
Toda-modification of the weight for the classical polynomials that correspond
to known explicit solutions for the Toda lattice, i.e., for Hermite, Laguerre,
Charlier, Meixner, Meixner-Pollaczek and Krawtchouk polynomials
Lacunary generating functions of Hermite polynomials and symbolic methods
We employ an umbral formalism to reformulate the theory of Hermite polynomials and the derivation of the associated lacunary generating functions
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