Some supercongruences on truncated hypergeometric series
نویسندگان
چکیده
منابع مشابه
Gaussian Hypergeometric series and supercongruences
Let p be an odd prime. In 1984, Greene introduced the notion of hypergeometric functions over finite fields. Special values of these functions have been of interest as they are related to the number of Fp points on algebraic varieties and to Fourier coefficients of modular forms. In this paper, we explicitly determine these functions modulo higher powers of p and discuss an application to super...
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Let p be an odd prime. The purpose of this paper is to refine methods of Ahlgren and Ono [2] and Kilbourn [13] in order to prove a general mod p congruence for the Gaussian hypergeometric series n+1Fn(λ) where n is an odd positive integer. As a result, we extend three recent supercongruences. The first is a result of Ono and Ahlgren [2] on a supercongruence for Apéry numbers which was conjectur...
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The purpose of this note is to obtain some congruences modulo a power of a prime p involving the truncated hypergeometric series p−1 � k=1 (x)k(1− x)k (1)k · 1 ka for a = 1 and a = 2. In the last section, the special case x = 1/2 is considered.
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Infinite series of the type ∞ ∑ n=1 ( 2 )n n 1 n! 2F1(−n, b; γ; y) are investigated. Closed-form sums are obtained for α a positive integer α = 1, 2, 3, . . . . The limiting case of b → ∞, after y is replaced with x2/b, leads to ∞ ∑ n=1 ( 2 )n n 1 n! 1F1(−n, γ, x2). This type of series appears in the first-order perturbation correction for the wavefunction of the generalized spiked harmonic osc...
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ژورنال
عنوان ژورنال: Journal of Difference Equations and Applications
سال: 2017
ISSN: 1023-6198,1563-5120
DOI: 10.1080/10236198.2017.1418863