Some Explicit Formulas for the Frobenius-Euler Polynomials of Higher Order

2017 ◽  
Vol 11 (2) ◽  
pp. 621-626 ◽  
Author(s):  
H. M. Srivastava ◽  
Mohamed Amine Boutiche ◽  
Mourad Rahmani
Keyword(s):  
Higher Order ◽  
Euler Polynomials ◽  
Explicit Formulas

scholarly journals Some explicit formulas for the generalized Frobenius-Euler polynomials of higher order

Filomat ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 211-220
Author(s):  
Hacène Belbachir ◽  
Nassira Souddi
Keyword(s):  
Higher Order ◽  
Euler Polynomials ◽  
Explicit Formulas

scholarly journals DETERMINING EQUATIONS FOR HIGHER-ORDER DECOMPOSITIONS OF EXPONENTIAL OPERATORS

1995 ◽  
Vol 09 (25) ◽  
pp. 3241-3268 ◽  
Author(s):  
ZENGO TSUBOI ◽  
MASUO SUZUKI
Keyword(s):  
General Scheme ◽  
Higher Order ◽  
Explicit Formulas ◽  
Decomposition Theory ◽  
Lyndon Words

The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of the coefficients are derived.

A Higher-Order Period Function and Its Application

2015 ◽  
Vol 25 (10) ◽  
pp. 1550140 ◽  
Author(s):  
Linping Peng ◽  
Lianghaolong Lu ◽  
Zhaosheng Feng
Keyword(s):  
Periodic Orbits ◽  
Upper Bound ◽  
Critical Period ◽  
Higher Order ◽  
Quadratic System ◽  
Critical Periods ◽  
Explicit Formulas ◽  
Period Function ◽  
Isochronous System ◽  
Isochronous Centers

This paper derives explicit formulas of the q th period bifurcation function for any perturbed isochronous system with a center, which improve and generalize the corresponding results in the literature. Based on these formulas to the perturbed quadratic and quintic rigidly isochronous centers, we prove that under any small homogeneous perturbations, for ε in any order, at most one critical period bifurcates from the periodic orbits of the unperturbed quadratic system. For ε in order of 1, 2, 3, 4 and 5, at most three critical periods bifurcate from the periodic orbits of the unperturbed quintic system. Moreover, in each case, the upper bound is sharp. Finally, a family of perturbed quintic rigidly isochronous centers is shown, which has three, for ε in any order, as the exact upper bound of the number of critical periods.

scholarly journals A note on the higher-order Frobenius-Euler polynomials and Sheffer sequences

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Dae San Kim ◽  
Taekyun Kim ◽  
Sang-Hun Lee ◽  
Seog-Hoon Rim
Keyword(s):  
Higher Order ◽  
Euler Polynomials ◽  
Sheffer Sequences

On modified higher-order q-Euler polynomials under S_5

2015 ◽  
Vol 9 ◽  
pp. 4171-4178
Author(s):  
Taekyun Kim ◽  
Jong Jin Seo
Keyword(s):  
Higher Order ◽  
Euler Polynomials

scholarly journals A three-term recurrence formula for the generalized Bernoulli polynomials

2021 ◽  
Vol 39 (6) ◽  
pp. 139-145
Author(s):  
Mohamed Amine Boutiche ◽  
Ghania Guettai ◽  
Mourad Rahmani ◽  
Madjid Sebaoui
Keyword(s):  
Recurrence Formula ◽  
Bernoulli Polynomials ◽  
Higher Order ◽  
Explicit Formulas ◽  
Whitney Numbers ◽  
Generalized Bernoulli Polynomials

In the present paper, we propose some new explicit formulas of the higher order Daehee polynomials in terms of the generalized r-Stirling and r-Whitney numbers of the second kind. As a consequence, we derive a three-term recurrence formula for the calculation of the generalized Bernoulli polynomials of order k.

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