scholarly journals Perfect powers in polynomial power sums

2021 ◽  
pp. 89-104
Author(s):  
Clemens Fuchs ◽  
Sebastian Heintze
Keyword(s):  
Power Sums

A concise proof of a theorem on products of power sums

1978 ◽  
Vol 6 (1) ◽  
pp. 11-17 ◽  
Author(s):  
P. S. Dwyer ◽  
N. N. Mikhail ◽  
D. S. Tracy
Keyword(s):  
Power Sums

scholarly journals IDENTITIES OF SYMMETRY FOR GENERALIZED TWISTED BERNOULLI POLYNOMIALS TWISTED BY RAMIFIED ROOTS OF UNITY

2014 ◽  
Vol 60 (1) ◽  
pp. 19-36
Author(s):  
Dae San Kim
Keyword(s):  
Generating Function ◽  
Bernoulli Polynomials ◽  
Roots Of Unity ◽  
Integral Expression ◽  
Power Sums ◽  
Exponential Generating Function

Abstract We derive eight identities of symmetry in three variables related to generalized twisted Bernoulli polynomials and generalized twisted power sums, both of which are twisted by ramified roots of unity. All of these are new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the p-adic integral expression of the generating function for the generalized twisted Bernoulli polynomials and the quotient of p-adic integrals that can be expressed as the exponential generating function for the generalized twisted power sums.

scholarly journals Some Identities of Symmetry for the Generalized Bernoulli Numbers and Polynomials

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Taekyun Kim ◽  
Seog-Hoon Rim ◽  
Byungje Lee
Keyword(s):  
Bernoulli Polynomials ◽  
Bernoulli Numbers ◽  
Bernoulli Numbers And Polynomials ◽  
Power Sums ◽  
Invariant Integral ◽  
Generalized Bernoulli Polynomials ◽  
Symmetric Properties

By the properties ofp-adic invariant integral onℤp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. From the symmetric properties ofp-adic invariant integral onℤp, we give some interesting relationship between the power sums and the generalized Bernoulli polynomials.

scholarly journals Derivation Power Sums of Even Integer Number Formula

2013 ◽  
Vol 10 (2) ◽  
pp. 301-318
Author(s):  
Baghdad Science Journal
Keyword(s):  
Programming Language ◽  
Computer Programming ◽  
Integer Number ◽  
Power Sums ◽  
Derivative Method ◽  
Number Formula ◽  
Microsoft Office ◽  
The Relationship

This paper included derivative method for the even r power sums of even integer numbers formula to approach high even (r+2) power sums of even integer numbers formula so on we can approach from derivative odd r power sums of even integer numbers formula to high odd (r+2) power sums of even integer numbers formula this derivative excellence have ability to used by computer programming language or any application like Microsoft Office Excel. Also this research discovered the relationship between r power sums of even integer numbers formula and both formulas for same power sums of odd integer numbers formula and for r power sums of all integer numbers formula in another way.

scholarly journals On a Positivity Conjecture in the Character Table of $S_n$

10.37236/8186 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Sheila Sundaram
Keyword(s):  
Lexicographic Order ◽  
Character Table ◽  
Power Sums ◽  
Special Cases ◽  
Schur Positive

In previous work of this author it was conjectured that the sum of power sums $p_\lambda,$ for partitions $\lambda$ ranging over an interval $[(1^n), \mu]$ in reverse lexicographic order, is Schur-positive. Here we investigate this conjecture and establish its truth in the following special cases: for $\mu\in [(n-4,1^4), (n)]$  or $\mu\in [(1^n), (3,1^{n-3})], $ or $\mu=(3, 2^k, 1^r)$ when $k\geq 1$ and $0\leq r\leq 2.$  Many new Schur positivity questions are presented.

scholarly journals Some Identities of Ordinary and Degenerate Bernoulli Numbers and Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 847 ◽  
Author(s):  
Dmitry V. Dolgy ◽  
Dae San Kim ◽  
Jongkyum Kwon ◽  
Taekyun Kim
Keyword(s):  
Random Variables ◽  
Infinite Family ◽  
Bernoulli Polynomials ◽  
Bernoulli Numbers ◽  
Higher Order ◽  
Integer Power ◽  
Bernoulli Numbers And Polynomials ◽  
Power Sums ◽  
Power Sum ◽  
Invariant Integrals

In this paper, we investigate some identities on Bernoulli numbers and polynomials and those on degenerate Bernoulli numbers and polynomials arising from certain p-adic invariant integrals on Z p . In particular, we derive various expressions for the polynomials associated with integer power sums, called integer power sum polynomials and also for their degenerate versions. Further, we compute the expectations of an infinite family of random variables which involve the degenerate Stirling polynomials of the second and some value of higher-order Bernoulli polynomials.

Sign in / Sign up

Export Citation Format

Share Document