Hypergeometric Functions, How Special Are They?
نویسندگان
چکیده
منابع مشابه
Hypergeometric Functions, How Special Are They?
where a, b, c are rational parameters. By specialization of the parameters, Euler obtained the various classical functions that were around at that time. For example, taking b = c = 1 gives us Newton’s binomial series for (1 − z)−a and taking a = b = 1/2, c = 3/2 gives us arcsin(√z)/√z. Finally, taking all parameters equal to 1 recovers the ordinary geometric series, which more or less explains...
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For an odd prime p, define Hp(z) = ∑ u,v(mod p) ( uv(1−u)(1−v)(1−uvz) p ) , where z is an integer (mod p) and the summands are Legendre symbols. The function Hp(z) was explicitly evaluated for z = 1 by Evans (1981) and for z = −1 by Greene and Stanton (1986). Koike (1992) determined Hp(1/4)(mod p), and Ono (1998) evaluated Hp(z) for z = 1/4,−1/8, and 1/64. This paper evaluates Hp(z) for infinit...
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ژورنال
عنوان ژورنال: Notices of the American Mathematical Society
سال: 2014
ISSN: 0002-9920,1088-9477
DOI: 10.1090/noti1065