A hypergeometric problem
نویسندگان
چکیده
منابع مشابه
A hypergeometric problem
For each n = 0, 1, 2, . . ., consider the following two rational functions: Rn(t) = (−1)n ( t + n 2 ) n ∏ l=1 (t − l)2 · n ∏ l=1 (t + n+ l)2 n ∏ l=0 (t + l)4 and R̃n(t) = n! n ∏ l=1 (t − l) n ∏ l=0 (t + l)2 n ∑ j=0 ( n j )2 (n+ j n ) n−1 ∏ l=0 (t − j+ l) n! . Problem 1. Prove that the following equality is valid for any n ≥ 0:
متن کاملThe Hypergeometric Coupon Collection Problem and its Dual
Suppose an urn contains M balls, of different types, which are removed from the urn in a uniform random manner. In the hypergeometric coupon collection problem, we are interested in the set of balls that have been removed at the moment when at least one ball of each type has been removed. In its dual, we are interested in the set of removed balls at the first moment that this set contains all o...
متن کاملAlgebraic A-hypergeometric functions
We formulate and prove a combinatorial criterion to decide if an A-hypergeometric system of differential equations has a full set of algebraic solutions or not. This criterion generalises the so-called interlacing criterion in the case of hypergeometric functions of one variable.
متن کاملA Hypergeometric Inequality
A sequence of coefficients that appeared in the evaluation of a rational integral has been shown to be unimodal. The original proof is based on a inequality for hypergeometric functions. A generalization is presented.
متن کاملA Subclass of Analytic Functions Associated with Hypergeometric Functions
In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2009
ISSN: 0377-0427
DOI: 10.1016/j.cam.2009.02.053