Abstract
In this article, the Laguerre-Gould Hopper based Bernoulli and Euler polynomials are introduced using operational methods. These polynomials are framed within the context of monomiality principle and their important properties are established. The operational rules and differential equations for these polynomials are also derived.
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The authors are thankful to the reviewer for useful suggestions towards the improvement of paper.
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Appendix
Appendix
It is important to note that several special polynomials follow as particular cases of the LGHP \(_{L} H_{n}^{(m,r)} (x,y,z).\)
We mention few of these polynomials in the following Table 1:
We remark that by selecting suitable values of the indices and variables (as in Table 1), we can introduce other new families of special polynomials. The results for these families are obtained by making use of the corresponding results derived in Sect. 2.
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Khan, S., Ali, M. (2016). On New Families Related to Bernoulli and Euler Polynomials. In: Satapathy, S., Raju, K., Mandal, J., Bhateja, V. (eds) Proceedings of the Second International Conference on Computer and Communication Technologies. Advances in Intelligent Systems and Computing, vol 381. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2526-3_57
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DOI: https://doi.org/10.1007/978-81-322-2526-3_57
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