Weinstein's functions and the askey-gasper identity
نویسندگان
چکیده
منابع مشابه
Weinstein's Functions and the Askey-gasper Identity Weinstein's Functions and the Askey-gasper Identity
In his 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums that was found by Askey and Gasper in 1973, published in 1976. In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system which (by Todorov and Wilf) was realize...
متن کاملWeinstein’s Functions and the Askey-Gasper Identity
In his 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums that was found by Askey and Gasper in 1973, published in 1976. In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system which (by Todorov and Wilf) was realize...
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In this talk I will present the conjecture and the main ideas that led to the proof. The proof of Lenard Weinstein (1991) [4] follows, and I will show how the two proofs are interrelated. Both proofs depend on polynomial systems that are directly related with the Koebe function. At this point algorithms of computer algebra come into the play, and I will give a computer demonstration how importa...
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The Bieberbach conjecture about the coefficients of univalent functions of the unit disk was formulated by Ludwig Bieberbach in 1916 [4]. The conjecture states that the coefficients of univalent functions are majorized by those of the Koebe function which maps the unit disk onto a radially slit plane. The Bieberbach conjecture was quite a difficult problem, and it was surprisingly proved by Lou...
متن کاملAskey-wilson Functions and Quantum Groups
Eigenfunctions of the Askey-Wilson second order q-difference operator for 0 < q < 1 and |q| = 1 are constructed as formal matrix coefficients of the principal series representation of the quantized universal enveloping algebra Uq(sl(2,C)). The eigenfunctions are in integral form and may be viewed as analogues of Euler’s integral representation for Gauss’ hypergeometric series. We show that for ...
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ژورنال
عنوان ژورنال: Integral Transforms and Special Functions
سال: 1997
ISSN: 1065-2469,1476-8291
DOI: 10.1080/10652469708819138