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,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2005-01-01
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| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/MPE.2005.215 |
| Summary: | 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 integral relations are also given in
this section for the Jacobi, Laguerre, and Bessel orthogonal
polynomials. Then we show that the rational orthogonal
polynomials can be a very suitable tool to compute the inverse
Laplace transform directly, with no additional calculation for
finding their roots. In this way, by applying infinite and finite
rational classical orthogonal polynomials, we give three basic
expansions of six ones as a sample for computation of inverse
Laplace transform. |
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| ISSN: | 1024-123X 1563-5147 |