Multi-Input Bernoulli-Polynomial WASD Neuronet

2019 ◽  
pp. 125-136
Author(s):  
Yunong Zhang ◽  
Dechao Chen ◽  
Chengxu Ye
Keyword(s):  
Bernoulli Polynomial

Single-Input Bernoulli-Polynomial WASD Neuronet

2019 ◽  
pp. 15-24
Author(s):  
Yunong Zhang ◽  
Dechao Chen ◽  
Chengxu Ye
Keyword(s):  
Bernoulli Polynomial ◽  
Single Input

Bernoulli and poly-Bernoulli polynomial convolutions and identities of p-adic Arakawa–Kaneko zeta functions

2016 ◽  
Vol 12 (05) ◽  
pp. 1295-1309 ◽  
Author(s):  
Paul Thomas Young
Keyword(s):  
Closed Form ◽  
Zeta Functions ◽  
Bernoulli Polynomials ◽  
Bernoulli Polynomial ◽  
Sum Formula

We evaluate the ordinary convolution of Bernoulli polynomials in closed form in terms of poly-Bernoulli polynomials. As applications we derive identities for [Formula: see text]-adic Arakawa–Kaneko zeta functions, including a [Formula: see text]-adic analogue of Ohno’s sum formula. These [Formula: see text]-adic identities serve to illustrate the relationships between real periods and their [Formula: see text]-adic analogues.

On reciprocity formulae for inhomogeneous and homogeneous Dedekind sums

1993 ◽  
Vol 114 (1) ◽  
pp. 9-24 ◽  
Author(s):  
R. R. Hall ◽  
J. C. Wilson
Keyword(s):  
Bernoulli Polynomial ◽  
Dedekind Sums ◽  
Linear Relations ◽  
Image Position ◽  
Number Of Authors

A number of authors, including Apostol [1], Carlitz [2], Mikolás [5] and Rademacher [9] have obtained linear relations for the Dedekind sums(the inhomogeneous sum) and the homogeneous sumHere denotes the periodic extension into ℝ of the Bernoulli polynomial Bm(X) on [0, 1] given by the relationwith the exception that we define

scholarly journals THE LOW ENERGY EFFECTIVE LAGRANGIAN FOR PHOTON INTERACTIONS IN ANY DIMENSION

1996 ◽  
Vol 11 (02) ◽  
pp. 253-269 ◽  
Author(s):  
A. RITZ ◽  
R. DELBOURGO
Keyword(s):  
Dimensional Space ◽  
Effective Interaction ◽  
Bernoulli Polynomial ◽  
Weak Field ◽  
Space Time ◽  
Low Energy ◽  
Time Dimension ◽  
Effective Lagrangian ◽  
Dimensional Space Time ◽  
Photon Interactions

The subject of low energy photon-photon scattering is considered in arbitrary-dimensional space-time and the interaction is widened to include scattering events involving an arbitrary number of photons. The effective interaction Lagrangian for these processes in QED has been determined in a manifestly invariant form. This generalization resolves the structure of the weak field Euler-Heisenberg Lagrangian and indicates that the component invariant functions have coefficients related not only to the space-time dimension but also to the coefficients of the Bernoulli polynomial.

A Note on Bernoulli-Goss Polynomials

1984 ◽  
Vol 27 (2) ◽  
pp. 179-184 ◽  
Author(s):  
K. Ireland ◽  
D. Small
Keyword(s):  
Closed Form ◽  
Existence Theorem ◽  
Function Fields ◽  
Bernoulli Polynomials ◽  
Bernoulli Polynomial ◽  
Computer Search ◽  
Quadratic Polynomials ◽  
Fermat's Equation

AbstractIn an important series of papers ([3], [4], [5]), (see also Rosen and Galovich [1], [2]), D. Goss has developed the arithmetic of cyclotomic function fields. In particular, he has introduced Bernoulli polynomials and proved a non-existence theorem for an analogue to Fermat’s equation for regular “exponent”. For each odd prime p and integer n, l ≤ n ≤ p2-2 we derive a closed form for the nth Bernoulli polynomial. Using this result a computer search for regular quadratic polynomials of the form x2-a was made. For primes less than or equal to 269 regular quadratics exist for p= 3, 5, 7, 13, 31.

scholarly journals Two congruences involving harmonic numbers with applications

2016 ◽  
Vol 12 (02) ◽  
pp. 527-539 ◽  
Author(s):  
Guo-Shuai Mao ◽  
Zhi-Wei Sun
Keyword(s):  
Bernoulli Polynomial ◽  
Combinatorial Identities ◽  
Harmonic Numbers

The harmonic numbers [Formula: see text] play important roles in mathematics. Let [Formula: see text] be a prime. With the help of some combinatorial identities, we establish the following two new congruences: [Formula: see text] and [Formula: see text] where [Formula: see text] denotes the Bernoulli polynomial of degree [Formula: see text]. As an application, we determine [Formula: see text] and [Formula: see text] modulo [Formula: see text], where [Formula: see text] with [Formula: see text].

scholarly journals Truncated euler polynomials

2018 ◽  
Vol 68 (3) ◽  
pp. 527-536 ◽  
Author(s):  
Takao Komatsu ◽  
Claudio Pita-Ruiz
Keyword(s):  
Bernoulli Polynomial ◽  
Euler Polynomial ◽  
Euler Polynomials

Abstract We define a truncated Euler polynomial Em,n(x) as a generalization of the classical Euler polynomial En(x). In this paper we give its some properties and relations with the hypergeometric Bernoulli polynomial.

Sign in / Sign up

Export Citation Format

Share Document