Differential and integral equations for the 2-iterated Bernoulli, 2-iterated Euler and Bernoulli–Euler polynomials
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Subuhi Khan
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.
Funding statement: This work has been done under Post-Doctoral Fellowship (Office Memo No.2/40(38)/2016/RD-II/1063) awarded to Mumtaz Riyasat by the National Board of Higher Mathematics, Department of Atomic Energy, Government of India, Mumbai.
Acknowledgements
The authors are thankful to the reviewer(s) for several useful comments and suggestions towards the improvement of this paper.
References
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Articles in the same Issue
- Frontmatter
- Stability analysis of delay integro-differential equations of HIV-1 infection model
- Oscillation of first-order differential equations with several non-monotone retarded arguments
- Idempotent matrices with invertible transpose
- Some algebraic aspects of the gluing of differential spaces
- Inner structure in real vector spaces
- Averaged semi-discrete scheme of sum-approximation for one nonlinear multi-dimensional integro-differential parabolic equation
- Differential and integral equations for the 2-iterated Bernoulli, 2-iterated Euler and Bernoulli–Euler polynomials
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- Approximation by modified Jain–Baskakov operators
- Carleson measure and Volterra type operators on weighted BMOA spaces
- The effect of perturbations of frames and fusion frames on their redundancies
- Predual spaces of generalized grand Morrey spaces over non-doubling measure spaces
- Trigonometric identities inspired by the atomic form factor
- W(Lp,Lq) boundedness of localization operators associated with the Stockwell transform
- Voronovskaja’s theorem for functions with exponential growth
- A quantitative Balian–Low theorem for higher dimensions
- Lp(·)–Lq(·) boundedness of some integral operators obtained by extrapolation techniques
- Statistical convergence of multiple sequences on a product time scale
Articles in the same Issue
- Frontmatter
- Stability analysis of delay integro-differential equations of HIV-1 infection model
- Oscillation of first-order differential equations with several non-monotone retarded arguments
- Idempotent matrices with invertible transpose
- Some algebraic aspects of the gluing of differential spaces
- Inner structure in real vector spaces
- Averaged semi-discrete scheme of sum-approximation for one nonlinear multi-dimensional integro-differential parabolic equation
- Differential and integral equations for the 2-iterated Bernoulli, 2-iterated Euler and Bernoulli–Euler polynomials
- On adjoint resolutions and dimensions of modules
- Approximation by modified Jain–Baskakov operators
- Carleson measure and Volterra type operators on weighted BMOA spaces
- The effect of perturbations of frames and fusion frames on their redundancies
- Predual spaces of generalized grand Morrey spaces over non-doubling measure spaces
- Trigonometric identities inspired by the atomic form factor
- W(Lp,Lq) boundedness of localization operators associated with the Stockwell transform
- Voronovskaja’s theorem for functions with exponential growth
- A quantitative Balian–Low theorem for higher dimensions
- Lp(·)–Lq(·) boundedness of some integral operators obtained by extrapolation techniques
- Statistical convergence of multiple sequences on a product time scale
