Orthogonal polynomials arising in the numerical evaluation of inverse Laplace transforms

On Rational Classical Orthogonal Polynomials and Their Application for Explicit Computation of Inverse Laplace Transforms

From the main equation (ax2 + bx + c)y′′ n (x) + (dx + e)y′ n(x)− n((n− 1)a+ d)yn(x) = 0, n∈ Z+, six finite and infinite classes of orthogonal polynomials can be extracted. In this work, first we have a survey on these classes, particularly on finite classes, and their corresponding rational orthogonal polynomials, which are generated by Mobius transform x = pz−1 + q, p = 0, q ∈ R. Some new int...

Numerical Inverse Laplace Transforms for Electrical Engineering Simulation

Numerical inverse Laplace transform (NILT) methods are widely used in various scientific areas, especially for a solution of respective differential equations. In field of an electrical engineering many various approaches have been considered so far, but mostly for a single variable (1D NILT), see at least (Brančík, 1999, 2007b; Cohen, 2007; Valsa & Brančík, 1998; Wu at al., 2001) from plenty o...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Laplace and Segal-bargmann Transforms on Hermitian Symmetric Spaces and Orthogonal Polynomials

Derangements and asymptotics of Laplace transforms of polynomials

We describe the behavior as n → ∞ of the Laplace transforms of P, where P a fixed complex polynomial. As a consequence we obtain a new elementary proof of an result of Gillis-Ismail-Offer [2] in the combinatorial theory of derangements. 1 Statement of the main results The generalized derangement problem in combinatorics can be formulated as follows. Suppose X is a finite set and ∼ is an equival...