p -adic subsets whose factorials satisfy a generalized Legendre formula
نویسندگان
چکیده
منابع مشابه
ON SOME p-ADIC SERIES WITH FACTORIALS
In the last nine years p-adic numbers have been successfully applied in various branches of theoretical and mathematical physics (for a review see [1-3]). One of the objects which we often encounter is a p-adic series. My interest in p-adic series is mainly motivated by the significant role they might play not only in pure but also in applied mathematics. It was initiated in 1987 [4] by an obse...
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متن کاملON p-ADIC WALDSPURGER FORMULA
conjugation, c, 5anti-cyclotomic p-adic L-function, L (π), 6Atkin–Serre operator, Θord, 13 canonical pairing, ( ,)A, 23convergent modular form, M(m,K), 14admissible, 15of finite tame level, M[ (m,K), 14stable, M[ (m,K)♥, 14universal, 15 distribution algebraA-related, D(A,K), 25ω-related, D(ω,K), 25π-related, D(π), 4 global Lubin–Tate different...
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During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured p-adic analogues to such formulae. Using a combination of ordinary and Gaussian hypergeometric series, we prove one of these conjectures. Mathematics Subject Classification (2000). Primary: 33C20; Secondary: 11S80.
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We present a simple new proof and a new generalization of Boole's formula n! = n j=1 (−1) n−j n j j n (n ∈ N).
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2008
ISSN: 0024-6093
DOI: 10.1112/blms/bdm090