Nonlinear integral-equation formulation of orthogonal polynomials
نویسندگان
چکیده
منابع مشابه
Nonlinear Integral Equation Formulation of Orthogonal Polynomials
The nonlinear integral equation P (x) = ∫ β α dy w(y)P (y)P (x + y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions P (x). For polynomial solutions, this nonlinear integral equation reduces to a finite set of coupled linear algebraic equations for the coefficients of the polynomials. Interestingly, the set of polynomial sol...
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Let c be a linear functional defined by its moments c(x) = ci for i = 0, 1, . . .. We proved that the nonlinear functional equations P (t) = c(P (x)P (x + t)) and P (t) = c(P (x)P (xt)) admit polynomial solutions which are the polynomials belonging to the family of formal orthogonal polynomials with respect to a linear functional related to c. Other types of nonlinear functional equations whose...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2006
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/40/1/f02