scholarly journals Expansion problems associated with the classical polynomials

1939 ◽  
pp. 244-273
Keyword(s):  
Classical Polynomials

scholarly journals Volterra-type convolution of classical polynomials

2019 ◽  
Vol 88 (319) ◽  
pp. 2351-2381 ◽  
Author(s):  
Ana F. Loureiro ◽  
Kuan Xu
Keyword(s):  
Volterra Type ◽  
Classical Polynomials

scholarly journals On polynomials of Sheffer type arising from a Cauchy problem

2003 ◽  
Vol 2003 (33) ◽  
pp. 2119-2137
Author(s):  
D. G. Meredith
Keyword(s):  
Cauchy Problem ◽  
Heat Conduction ◽  
Parabolic Equations ◽  
Analytic Solution ◽  
Heat Conduction Problem ◽  
Laguerre Polynomials ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Operator Calculus ◽  
Classical Polynomials

A new sequence of eigenfunctions is developed and studied in depth. These theta polynomials are derived from a recent analytic solution of the canonical Cauchy problem for parabolic equations, namely, the inverse heat conduction problem. By appealing to the methods of the operator calculus, it is possible to categorize the new functions as polynomials of binomial and Sheffer types. The connection of the new set with the classical polynomials of Laguerre is carefully examined. Some integral relations involving the Laguerre polynomials and the theta polynomials are presented along with a number of binomial identities. The inverse heat conduction problem is revisited and an analytic solution depending on the generalized theta polynomials is presented.

Fibonacci Analogs of the Classical Polynomials

1975 ◽  
Vol 48 (3) ◽  
pp. 123-130 ◽  
Author(s):  
A. G. Shannon
Keyword(s):  
Classical Polynomials

On integrals involving classical polynomials

1968 ◽  
Vol 64 (2) ◽  
pp. 417-420 ◽  
Author(s):  
G. K. Dhawan
Keyword(s):  
Classical Polynomials ◽  
Image Position

We know ((6), p. 343) thatandwhere α,β,α′ and β′ are parameters such thatConsider

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