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Title of article :
Solving connection and linearization problems within the Askey scheme and its q-analogue via inversion formulas
Author/Authors :
Area، نويسنده , , I. and Godoy، نويسنده , , E. and Ronveaux، نويسنده , , A. and Zarzo، نويسنده , , A.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2001
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Abstract :
For the polynomial families {Pn(x)}n belonging to the Askey scheme or to its q-analogue, the hypergeometric representation provides a natural expansion of the form Pn(x)=∑m=0nDm(n)θm(x), where the expanding basis θm(x) is, in general, a product of Pochhammer symbols or q-shifted factorials. In this paper we solve the corresponding inversion problem, i.e. we compute the coefficients Im(n) in the expansion θn(x)=∑m=0nIm(n)Pm(x), which are then used as a tool for solving any connection and linearization problem within the Askey scheme and its q-analogue. Extensions of this approach for polynomials outside these two schemes are also given.
Keywords :
Connection problems , Inversion problems , Hypergeometric polynomials , Basic hypergeometric polynomials , Linearization problems
Journal title :
Journal of Computational and Applied Mathematics
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Link To Document :