Hermite Polynomials
A Multinomial Theorem for Hermite Polynomials and Financial Applications
... The main assumption made throughout the paper is the existence of a payoff’s or probability density func- tion’s expansion in the basis of Hermite polynomials. Although this is quite restrictive (it implies ...
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The Relativistic Hermite Polynomials and the Wave Equation
... relativistic Hermite polynomials in terms of the proper Gauss hypergeometric function, deducible from ...order Hermite-Lorentzian solutions of the 2D wave ...
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A Note on the (p, q)-Hermite Polynomials
... the Hermite polynomials based on the (p; q)- numbers via an exponential generating function and investigate several properties and relations for mentioned polynomials including derivative property, ...
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Some Properties of the Hermite Polynomials and Their Squares and Generating Functions
... the Hermite polyno- mials and their squares, present explicit formulas for higher order derivatives of the generating functions of the Hermite polynomials and their squares, which can be viewed as ...
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2. Generalized $q$-Hermite Polynomials and the $q$-Dunkl Heat Equation
... q-Hermite polynomials are con- structed. Several properties of these polynomials, and an explicit relations con- necting them with little q-Laguerre and q-Laguerre polynomials are ...heat ...
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On a Class of Humbert-Hermite Polynomials
... In (1.20), if we put a = 1, b = c = 2, d = − 1, e = − 2 and g = 1, then we get a generating relation (1.18) studied by Djordjevi´ c [9]. For y = 1, e = 2 and c = 0, we get a generating relation (1.16) studied by Pathan ...
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Associated Hermite Polynomials Related to Parabolic Cylinder Functions
... mite polynomials and for their derivative and the differential equation for them are derived in ...Associated Hermite polynomials with involved Jacobi polynomials at argument zero are given ...
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The Hermite polynomials and the Bessel functions from a general point of view
... We introduce new families of Hermite polynomials and of Bessel functions from a point of view involving the use of nonexponential generating functions. We study their relevant recurrence relations and show ...
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Composite Hermite and Anti Hermite Polynomials
... eigenfunctions, Hermite polynomials and the corresponding positive eigenvalues, while the anti-normal order form (3b) yields anti-eigenfunctions, anti-Hermite polynomials and the corresponding ...
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Higher order Bernoulli, Euler and Hermite polynomials
... Kim et al Advances in Difference Equations 2013, 2013 103 http //www advancesindifferenceequations com/content/2013/1/103 R E V IE W Open Access Higher order Bernoulli, Euler and Hermite polynomials D[.] ...
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A characterization of the Rogers q hermite polynomials
... By an orthogonal polynomial set OPS we shall mean those polynomial sets which satisfy three term recurrence relation of the form.. By Favard’s theorem [7] this is equivalent to the exist[r] ...
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Sumudu Transformation or What Else Can Laplace Transformation Do
... Belgacem and coauthors, e.g., [2] [3] [4] [5] [6] and many others, e.g., [7]. The article [2] contains basic examples of Sumudu transforms of functions. Since Laplace transformations are widely applied in mathematics for ...
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Vol 2, No 6 (2011)
... So, according to the number of uncertain model inputs, n = 2, 3, and 4, the number of unknown coefficients to be determined in the polynomial chaos expansion can be obtained using Eqs.(4) and (5) as {6, 10 and 15} and ...
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Hermite based unified Apostol Bernoulli, Euler and Genocchi polynomials
... In this paper, we introduce a unified family of Hermite-based Apostol-Bernoulli, Euler and Genocchi polynomials. We obtain some symmetry identities between these polynomials and the generalized sum of ...
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... q-Hermite polynomials are special or limiting case of the orthogonal poly- nomials as they contain no parameter other than q and appears to be at the bottom of a hierarchy of the classical ...
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7.Summation formula for generalized discrete $q$-Hermite II polynomials
... Srivastava and Jain [12, 6], investigated multilinear generating functions for q- Hermite, q-Laguerre polynomials and other special functions. Relevant connections of these multilinear generating functions ...
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... Special polynomials and numbers possess a lot of importances in many …elds of mathematics, physics, engineering and other related disciplines including the topics such as di¤erential equations, mathematical ...
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Generating Functions for Products of Special Laguerre 2D and Hermite 2D Polynomials
... and Hermite 2D polynomials was solved in [9]-[12] ...2D polynomials or of a Laguerre 2D and a Hermite 2D ...these polynomials are fairly complicated ...2D polynomials, for ...
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New Extension of Unified Family Apostol Type of Polynomials and Numbers
... Apostol-type polynomials and numbers based on results given in [1] ...these polynomials and obtain some relationships between the Jacobi polynomials, Laguerre polynomials, Hermite ...
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A NOTE ON TYPE 2 DEGENERATE MULTI-POLY-BERNOULLI POLYNOMIALS AND NUMBERS
... many polynomials, theorems, numbers ...and polynomials. For example, the degenerate Hermite polynomials in [3], the degenerate Hermite-Bernoulli poynomials and numbers in [4], the ...
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