New formulae for higher order derivatives and applications (Q732148)
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scientific article; zbMATH DE number 5612610
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | New formulae for higher order derivatives and applications |
scientific article; zbMATH DE number 5612610 |
Statements
New formulae for higher order derivatives and applications (English)
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9 October 2009
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New formulae for the analytical development of higher order derivatives are presented. The formulae are analytic and exact and represent the \(k\)-th derivative as a discrete sum of \(k+1\) terms. The coefficients occurring in the sums can be computed by recursion. Examples are given for Legendre, Hermite, and Bessel functions and for Chebyshev polynomials. Further applications to differential equations are outlined.
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higher order derivatives
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special functions
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Bessel functions
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numerical integration
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differential equations
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Legendre function
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Hermite function
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