Series expansions for computing Bessel functions of variable order on bounded intervals (Q1587037)
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scientific article; zbMATH DE number 1534775
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Series expansions for computing Bessel functions of variable order on bounded intervals |
scientific article; zbMATH DE number 1534775 |
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Series expansions for computing Bessel functions of variable order on bounded intervals (English)
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22 November 2000
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Series of the the Bessel function \(J_\lambda(w)\) are considered by using the Hadamard product of power series. The rate of convergence is discussed, in particular when series in terms of Gegenbauer and Chebyshev polynomials are considered. A comparison is made with the Taylor series of the Bessel function in connection with cancellation problems and efficiency. The method is also used for a confluent hypergeometric function.
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Bessel functions
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series expansions
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Hadamard product
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convergence
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confluent hypergeometric functions
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Gegenbauer polynomials
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Chebyshev polynomials
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Taylor series
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