Results 71 to 80 of about 47,919 (237)

Derivatives of tangent function and tangent numbers

, 2015
In the paper, by induction, the Fa\`a di Bruno formula, and some techniques in the theory of complex functions, the author finds explicit formulas for higher order derivatives of the tangent and cotangent functions as well as powers of the sine and ...
Bourbaki, Boyadzhiev, Comtet, Daboul, Dominici, Feng Qi, Guo, Guo, Guo, Guo, Guo, Guo, Guo, Guo, Hoffman, Hoffman, Luo, Luo, Ma, Ma, Ma, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Remmert, Schwatt, Schwatt, Wei, Xu, Zhang   +37 more
core   +1 more source

A Note on the q-Euler Numbers and Polynomials with Weak Weight α

Journal of Applied Mathematics, 2011
In this paper we construct a new type of q-Bernstein polyno- mials related to q-Euler numbers and polynomials with weak weight ; E ( ) n;q , E ( ) n;q (x) respectively. Some interesting results and relationships are obtained.
H. Lee, N. Jung, C. Ryoo
semanticscholar   +1 more source

Analytic continuation of q-Euler numbers and polynomials

Applied Mathematics Letters, 2008
In this paper we study that the $q$-Euler numbers and polynomials are analytically continued to $E_q(s)$. A new formula for the Euler's $q$-Zeta function $ζ_{E,q}(s)$ in terms of nested series of $ζ_{E,q}(n)$ is derived. Finally we introduce the new concept of the dynamics of analytically continued $q$-Euler numbers and polynomials.
openaire   +3 more sources

Apostol type (p, q): Frobenius-Euler polynomials and numbers [PDF]

Kragujevac Journal of Mathematics, 2018
Summary: In the present paper, we introduce \((p,q)\)-extension of Apostol type Frobenius-Euler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, difference equations, derivative properties, recurrence relations and so on.
Duran, Ugur, Acikgoz, Mehmet
openaire   +5 more sources

A Hybrid Semi‐Inverse Variational and Machine Learning Approach for the Schrödinger Equation

Advanced Physics Research, EarlyView.
A hybrid semi‐inverse variational and machine‐learning framework is presented for solving the Schrödinger equation with complex quantum potentials. Physics‐based variational solutions generate high‐quality training data, enabling Random Forest and Neural Network models to deliver near‐perfect energy predictions.
Khalid Reggab, Houssam Eddine Hailouf, Kingsley Onyebuchi Obodo, Mireille Megnidio‐Tchoukouegno, Mohammed Benali Kanoun, Souraya Goumri‐Said   +5 more
wiley   +1 more source

Anharmonic polynomial generalizations of the numbers of Bernoulli and Euler [PDF]

Transactions of the American Mathematical Society, 1922
We consider twelve infinite systems of polynomials in z which for z = 1 degenerate either to the numbers of Bernoulli or Euler, or to others simply dependent upon these. The first part proceeds from the definition of anharmonic polynomials to the specific twelve systems discussed; the second presents an adaptation of the symbolic calculus of Blissard ...
openaire   +1 more source

Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
wiley   +1 more source

Degenerate Fubini-Type Polynomials and Numbers, Degenerate Apostol–Bernoulli Polynomials and Numbers, and Degenerate Apostol–Euler Polynomials and Numbers

Axioms, 2022
In this paper, by introducing degenerate Fubini-type polynomials, with the help of the Faà di Bruno formula and some properties of partial Bell polynomials, the authors provide several new explicit formulas and recurrence relations for Fubini-type ...
Siqintuya Jin, Muhammet Cihat Dağli, Feng Qi   +2 more
doaj   +1 more source

Local Polynomial Regression and Filtering for a Versatile Mesh‐Free PDE Solver

International Journal for Numerical Methods in Fluids, EarlyView.
A high‐order, mesh‐free finite difference method for solving differential equations is presented. Both derivative approximation and scheme stabilisation is carried out by parametric or non‐parametric local polynomial regression, making the resulting numerical method accurate, simple and versatile. Numerous numerical benchmark tests are investigated for
Alberto M. Gambaruto
wiley   +1 more source

Note on the q-Extension of Barnes' Type Multiple Euler Polynomials

Journal of Inequalities and Applications, 2009
We construct the q-Euler numbers and polynomials of higher order, which are related to Barnes' type multiple Euler polynomials. We also derive many properties and formulae for our q-Euler polynomials of higher order by using the multiple integral ...
Leechae Jang, Taekyun Kim, Young-Hee Kim, Kyung-Won Hwang   +3 more
doaj   +1 more source