Turkish Journal of Mathematics
DOI
10.3906/mat-2005-116
Abstract
By applying Laplace differential operator to harmonic conjugate components of the analytic functions and using Wirtinger derivatives, some identities and relations including Bernoulli and Euler polynomials and numbers are obtained. Next, using the Legendre identity, trigonometric functions and the Dirichlet kernel, some formulas and relations involving Bernoulli and Euler numbers, cosine-type Bernoulli and Euler polynomials, and sine-type Bernoulli and Euler polynomials are driven. Then, by using the generating functions method and the well-known Euler identity, many new identities, formulas, and combinatorial sums among the Fibonacci numbers and polynomials, the Lucas numbers and polynomials, the Chebyshev polynomials, and Bernoulli and Euler type polynomials are given. Finally, some infinite series representations for these special numbers and polynomials and their numerical examples are presented.
Keywords
Bernoulli and Euler type numbers and polynomials, Chebyshev polynomials, Fibonacci and Lucas polynomials, Generating functions, Harmonic and trigonometric functions, Laplace operator
First Page
2217
Last Page
2240
Recommended Citation
KILAR, NESLİHAN and ŞİMŞEK, YILMAZ
(2020)
"A special approach to derive new formulas for some special numbers and polynomials,"
Turkish Journal of Mathematics: Vol. 44:
No.
6, Article 19.
https://doi.org/10.3906/mat-2005-116
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss6/19
