منابع مشابه
Hypergeometric Periods for a Tame Polynomial
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This paper deals with regular singular generalized q-hypergeometric equations with either “large” or “small” Galois groups. In particular, we consider the fundamental problem of finding appropriate Galoisian substitutes for the usual notion of local monodromy.
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1. Mittag-Leffler's polynomial gn(z) has the orthogonal property fgm(-ix)gn(ix)dx/xsh(x) = m $ n m > 0-co =-2/n m=n n>O. (1.1) This is readily obtained by inverting the integral representation' co gn(ix) = (1/ir) sin (irx)f exu (tanh '/2u)ndu/sh u n > 1 (1.2)-co0 by means of Fourier's inversion formula. The resulting equation co cosech u (tanh 1/2u)n = 1/2 e-iux cosech (irx)gn(ix)dx (1.3)-OD th...
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The hypergeometric type differential equations of the second order with polynomial coefficients and their systems are considered. The realization of the Lanczos Tau Method with minimal residue is proposed for the approximate solution of the second order differential equations with polynomial coefficients. The scheme of Tau method is extended for the systems of hypergeometric type differential e...
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Consider an operator dQ(f) = d dxk (Q(x)f(x)) where Q(x) is some fixed polynomial of degree k. One can easily see that dQ has exactly one polynomial eigenfunction pn(x) in each degree n ≥ 0 and its eigenvalue λn,k equals (n+k)! n! . A more intriguing fact is that all zeros of pn(x) lie in the convex hull of the set of zeros to Q(x). In particular, if Q(x) has only real zeros then each pn(x) enj...
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 1967
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-19-2-177-184