Relations of the Extended Voigt Function with Other Families of Polynomials and Numbers
Author presents a new family of generalized Voigt functions related to recently introduced k-Fibonacci–Hermite numbers, h(x)-Fibonacci–Hermite polynomials, Lucas–Hermite numbers and h(x)-Lucas–Hermite polynomials where h(x) is a polynomial with real coefficients. The multivariable extensions of these results provide a natural generalization and unification of integral representations which may be viewed as a new relationship for the product of two different families of Lucas and Hermite polynomials. Some interesting explicit series representations, integrals and identities are obtained. The resulting formulas allow a considerable unification of various special results which appear in the literature.
The first author M. A. Pathan would like to thank the Department of Science and Technology, Government of India, for the financial assistance for this work under project number SR/S4/MS:794/12.
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