مقالة علمية
A Family of Generalized Legendre-Based Apostol-Type Polynomials

Talha Usman.


مرفقات :
(1)

 

A Family of Generalized Legendre-Based Apostol-Type Polynomials

Talha Usman.

Numerous polynomials, their extensions, and variations have been thoroughly explored, owing to their potential applications in a wide variety of research fields. The purpose of this work is to provide a unified family of Legendre-based generalized Apostol-Bernoulli, Apostol-Euler, and Apostol-Genocchi polynomials, with appropriate constraints for the Maclaurin series. Then we look at the formulae and identities that are involved, including an integral formula, differential formulas, addition formulas, implicit summation formulas, and general symmetry identities. We also provide an explicit representation for these new polynomials. Due to the generality of the findings given here, various formulae and identities for relatively simple polynomials and numbers, such as generalized Bernoulli, Euler, and Genocchi numbers and polynomials, are indicated to be deducible. Furthermore, we employ the umbral calculus theory to offer some additional formulae for these new polynomials.

Numerous polynomials, their extensions, and variations have been thoroughly explored, owing to their potential applications in a wide variety of research fields. The purpose of this work is to provide a unified family of Legendre-based generalized Apostol-Bernoulli, Apostol-Euler, and Apostol-Gen...

مادة فرعية

المؤلف : Talha Usman.

مؤلف مشارك : Khan, Nabiullah
Aman, Mohd
Choi, Junesang

بيانات النشر : axioms، 2022مـ.

التصنيف الموضوعي : العلوم التطبيقية|الهندسة .

المواضيع : Legendre-based Apostol Bernoulli polynomials .

Legendre-based Apostol Euler polynomials .

summation formulae .

المصدر : MDPI : .

لا توجد تقييمات للمادة