Lacunary Recurrent Relations with Gaps of Length Four for the Bernoulli and Euler Polynomials
نویسندگان
چکیده
We obtain lacunary recurrent relations with gaps of length four for the Bernoulli and Euler polynomials and, as a consequence, known new numbers.
منابع مشابه
Padé Approximation and Apostol-Bernoulli and -Euler Polynomials
Using the Padé approximation of the exponential function, we obtain recurrence relations between Apostol-Bernoulli and between Apostol-Euler polynomials. As applications, we derive some new lacunary recurrence relations for Bernoulli and Euler polynomials with gap of length 4 and lacunary relations for Bernoulli and Euler numbers with gap of length 6.
متن کاملSome identities and recurrences relations for the q-Bernoulli and q-Euler polynomials
In this article we prove some relations between two-variable q-Bernoulli polynomials and two-variable q-Euler polynomials. By using the equality eq (z)Eq (−z) = 1, we give an identity for the two-variable qGenocchi polynomials. Also, we obtain an identity for the two-variable q-Bernoulli polynomials. Furthermore, we prove two theorems which are analogues of the q-extension Srivastava-Pinter add...
متن کاملArith . IDENTITIES CONCERNING BERNOULLI AND EULER POLYNOMIALS
We establish two general identities for Bernoulli and Euler polynomials, which are of a new type and have many consequences. The most striking result in this paper is as follows: If n is a positive integer, r + s + t = n and x + y + z = 1, then we have r s t x y n + s t r y z n + t r s z x n = 0 where s t x y n := n k=0 (−1) k s k t n − k B n−k (x)B k (y). It is interesting to compare this with...
متن کاملNew identities involving Bernoulli and Euler polynomials
Using the finite difference calculus and differentiation, we obtain several new identities for Bernoulli and Euler polynomials; some extend Miki’s and Matiyasevich’s identities, while others generalize a symmetric relation observed by Woodcock and some results due to Sun.
متن کاملOn Identities Involving Bernoulli and Euler Polynomials
A class of identities satisfied by both Bernoulli and Euler polynomials is established. Recurrence relations for Bernoulli and Euler numbers are derived.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2023
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-023-06371-8