On asymptotic constants related to products of Bernoulli numbers and factorials
نویسنده
چکیده
We discuss the asymptotic expansions of certain products of Bernoulli numbers and factorials, e.g., n ∏
منابع مشابه
Bernoulli numbers and generalized factorial sums
We prove a pair of identities expressing Bernoulli numbers and Bernoulli numbers of the second kind as sums of generalized falling factorials. These are derived from an expression for the Mahler coefficients of degenerate Bernoulli numbers. As corollaries several unusual identities and congruences are derived.
متن کاملCongruences for degenerate number sequences
The degenerate Stirling numbers and degenerate Eulerian polynomials are intimately connected to the arithmetic of generalized factorials. In this article we show that these numbers and similar sequences may in fact be expressed as p-adic integrals of generalized factorials. As an application of this identiication we deduce systems of congruences which are analogues and generalizations of the Ku...
متن کاملThe Universal Kummer Congruences
Let p be a prime. In this paper, we present detailed p-adic analysis to factorials and double factorials and their congruences. We give good bounds for the p-adic sizes of the coefficients of the divided universal Bernoulli number B̂n n when n is divisible by p−1. Using these we then establish the universal Kummer congruences modulo powers of a prime p for the divided universal Bernoulli numbers...
متن کاملMathematical Constants and Sequences
Basic math constants Derived from the basic ones ... from 0 and 1 ... from i ... from 1 and i ... from π ... from e ... from e and π ... from γ ... from Φ Named real math constants Other notable real constants Notable integer numbers Named/notable functions on N Named/notable integer sequences Related to Factorials Related to Hamming weight Related to Powers Related to Divisors Related to Aliqu...
متن کاملExponential Sums and Congruences with Factorials
We estimate the number of solutions of certain diagonal congruences involving factorials. We use these results to bound exponential sums with products of two factorials n!m! and also derive asymptotic formulas for the number of solutions of various congruences with factorials. For example, we prove that the products of two factorials n!m! with max{n,m} < p1/2+ε are uniformly distributed modulo ...
متن کامل