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Differential and integral equations for the 2-iterated Bernoulli, 2-iterated Euler and Bernoulli–Euler polynomials
Georgian Mathematical Journal ( IF 0.7 ) Pub Date : 2020-09-01 , DOI: 10.1515/gmj-2018-0062
Subuhi Khan 1 , Mumtaz Riyasat 1
Affiliation  

Abstract The main goal of this article is to derive differential and associated integral equations for some 2-iterated and mixed type special polynomial families. By using the factorization method, the recurrence relations and differential equations are derived for the 2-iterated Bernoulli, 2-iterated Euler and Bernoulli–Euler polynomials. The Volterra integral equations for these polynomial families are also established. The graphical representation of these 2-iterated and mixed polynomials is presented. The zeros of these polynomials are investigated for certain values of the index n using numerical computation. The approximate solutions of the real zeros of these polynomials are also given.

中文翻译:

2 次迭代 Bernoulli、2 次迭代 Euler 和 Bernoulli-Euler 多项式的微分方程和积分方程

摘要 本文的主要目标是推导出一些二次迭代和混合类型的特殊多项式族的微分方程和相关积分方程。通过使用分解方法,推导出了 2 次迭代伯努利、2 次迭代欧拉和伯努利-欧拉多项式的递推关系和微分方程。还建立了这些多项式族的 Volterra 积分方程。给出了这些 2 次迭代和混合多项式的图形表示。使用数值计算针对索引 n 的某些值研究这些多项式的零点。还给出了这些多项式的实零点的近似解。
更新日期:2020-09-01
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