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Explicit Formulas for Bernoulli Numbers

✍ Scribed by H. W. Gould

Book ID
111951712
Publisher
Mathematical Association of America
Year
1972
Tongue
English
Weight
929 KB
Volume
79
Category
Article
ISSN
0002-9890

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πŸ“œ SIMILAR VOLUMES

Explicit formulas for degenerate Bernoul
Explicit formulas for degenerate Bernoulli numbers
✍ F.T. Howard πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 380 KB

The 'degenerate' Bernoulli numbers tim(2) can be defined by means of the exponential generating function x((1 + 2x) 1/~ -1)-1. L. Carlitz proved an analogue of the Staudt-Clausen theorem for these numbers, and he showed that/3m(2) is a polynomial in 2 of degree ~< m. In this paper we find explicit f

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We employ the basic properties for the Hasse-TeichmΓΌller derivatives to give simple proofs of known explicit formulae for Bernoulli numbers (of higher order) and then obtain some parallel results for their counterparts in positive characteristic.

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✍ Zhi-Hong Sun πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 292 KB

Let {B.(x)} be the well-known Bernoulli polynemials. It is the purpose of this paper to determine pB~p-t~+b(x)modp ", where p is a prime, k, b nonnegative integers and x a rational p-integer. It is interesting to investigate arithmetic properties of {B,} and {Bn(x)}. For the work on this line one ma