[PDF] Top 20 Classical 2 orthogonal polynomials and differential equations
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Classical 2 orthogonal polynomials and differential equations
... and 1, depending generally on n. The main result is that the coefficient associated with highest derivative can be written as the product of 2 polynomials of which one is of degree ≤ 3 and independent of n. ... See full document
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A characterization of the four Chebyshev orthogonal families
... Section 2, first we recall some properties concerning the classical orthogonal polynomials and we present the Bernstein orthogonal ...nonclassical orthogonal polynomials, ... See full document
9
Solving singular integral equations by using orthogonal polynomials
... second function of both variables) for some m ≥ 0, 0 < ν ≤ 1, and they are approximated by a finite Chebyshev series of order M . Moreover, for sufficiently large value of M, the homogeneous equation corresponding to ... See full document
15
A method for fractional Volterra integro differential equations by Laguerre polynomials
... This paper is organized as follows: In Sect. 2, the main matrix relations of the terms in Eq. (1) are established. In Sect. 3, the collocation method which is used to find the solution is introduced. In Sect. 4, ... See full document
11
Solution of Fractional Differential Equations By Adomian Decomposition Method With Chebyshev Polynomials
... 1, 2, 3, 4 introduced a powerful method named as Adomian decomposition method (ADM) for solving linear and nonlinear functional ...nonlinear equations and considerable interest in solving fractional ... See full document
9
On the 2 orthogonal polynomials and the generalized birth and death processes
... Proposition 2.1. Let be a “generalized” birth and death process, where the transition prob- abilities are given by (1.2), then these probabilities satisfy two systems of differential recur- rence relations called ... See full document
12
Properties of Solutions of Complex Differential Equations in the Unit Disc
... Throughout this paper, we assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna’s value distribution theory on the complex plane and in the unit disc ∆ = {z : |z| ... See full document
15
Numerical Solutions of Volterra Equations Using Galerkin Method with Certain Orthogonal Polynomials
... u x − ∫ u t t = ≤ ≤ x (23) The exact solution is u x ( ) = e 1 x ( + x ) . Results is shown in Table 3 for n = 2 and 3. The maximum abso- lute errors obtain in the order for 10 − 3 and 10 − 4 for n = 2 and ... See full document
7
A class of orthogonal polynomials of a new type
... Here we see that for different values of v we shall obtain m different differential equations, but solutions of these differential equations are orthogonal in the.. is obviously replaced[r] ... See full document
10
Differential equations for the extended 2D Bernoulli and Euler polynomials
... Bernoulli polynomials, by means of Hermite-Kampé de Fériet (or Gould Hopper) polynomials and Bernoulli ...ential equations and shift operators for the extended D Bernoulli polynomials by us- ... See full document
16
Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds
... The classical linearization problem concerns with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of ...Chebyshev polynomials of the first, ... See full document
16
Kernel Polynomial of 2-Orthogonal Sequence
... of 2-orthogonal polynomials is ...the 2-orthogonality, the strictly 2-quasi-orthogonality, the ...the classical 2-orthogonality properties under some ... See full document
8
An example of nonsymmetric semi classical form of class s=1; generalization of a case of Jacobi sequence
... [5] P. Maroni, Sur la suite de polynômes orthogonaux associée à la forme u = δ c +λ(x −c) −1 L [On the sequence of orthogonal polynomials associated with the form u = δ c + λ(x− c) −1 L], Period. Math. ... See full document
17
Solution of Fractional Differential Equations By Adomian Decomposition Method With Chebyshev Polynomials
... of differential equations by orthogonal polynomial has become extreemly ...important polynomials which is widely used 11, 12, 13 to solve various linear and nonlinear differential ... See full document
9
Some identities of Laguerre polynomials arising from differential equations
... differential equations) have wide applications in such diverse areas as fluid mechanics, plasma physics, dynamical processes and finance, ...differential equations due to their high accuracy and employ ... See full document
9
Classical orthogonal polynomials and Leverrier Faddeev algorithm for the matrix pencils sE−A
... the classical Leverrier-Faddeev algorithm using families of classical orthogonal polynomials following our previous contribution [2] when instead of a singular matrix E we used I n ... See full document
13
8. The $\textbf{D}_{u}$-Classical Orthogonal Polynomials
... give orthogonal polynomials generalizing (by their prop- erties and their characterizations) the classical orthogonal polynomials, but gener- ally it is difficult to explicitly ... See full document
33
A Comparative Study of Adomain Decompostion Method and He Laplace Method
... An important conclusion can be made here. Adomain decomposition method for solving nonlinear ordinary and partial differential equations, the same problems are solved by He-Laplace method. Adomain ... See full document
13
On \((p,q)\) classical orthogonal polynomials and their characterization theorems
... q)-difference equations of hypergeometric type are introduced, in the sense that the (p, q)-difference of a solution of the equation is solution of an equation of the same ...the orthogonal polynomial solu- ... See full document
17
Extended Jacobi and Laguerre Functions and their Applications
... introduce orthogonal functions that are solutions of a non-classical Sturm-Liouville ...of orthogonal polynomials which satisfy the Sturm-Liouville problems but also there are a lot of ... See full document
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