| Autor: |
Wolfgang Schweizer |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Special Functions in Physics with MATLAB ISBN: 9783030642310 |
| DOI: |
10.1007/978-3-030-64232-7_15 |
| Popis: |
Topics of this chapter are fundamental aspects of orthogonal polynomials. Orthogonal polynomials play a prominent role for many applications in physics. In this chapter we discuss in detail Jacobi polynomials and Gegenbauer polynomials in the complex domain and generalizations for non-integer degrees. The evaluation is either based on recurrence equations or on the hypergeometric function. The computation of the polynomial roots is based on the eigenvalues of the corresponding Jacobi matrix. For all evaluations m-codes are available for download. With respect to computational aspects a superclass is derived with various methods from creating plots up to integrating weighted scalar products of orthogonal polynomials. Due to the huge number of orthogonal polynomials an additional class serving as container for arbitrary orthogonal polynomials is derived. As an application Zernike polynomials are presented. The corresponding programming codes are available for download. |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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