Difference between revisions of "Bessel Functions"
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Bessel Functions are used in engineering models to describe harmonic vibrations in cylindrical systems, such as electromagnetic waves in a cylindrical waveguide, sound vibrations in a circular membrane, or heat conduction in a cylindrical object. Analytica exposes the following Bessel functions: | Bessel Functions are used in engineering models to describe harmonic vibrations in cylindrical systems, such as electromagnetic waves in a cylindrical waveguide, sound vibrations in a circular membrane, or heat conduction in a cylindrical object. Analytica exposes the following Bessel functions: | ||
| − | : | + | :<code>BesselJ(x, n)</code>: Bessel function of the first kind |
| − | : | + | :<code>BesselY(x, n)</code>: Bessel function of the second kind |
| − | : | + | :<code>BesselK(x, n)</code>: Modified Bessel function of the first kind |
| − | : | + | :<code>BesselY(x, n)</code>: Modified Bessel function of the second kind |
| − | In each case, «n» is the order of the Bessel function and can be zero or greater. Analytica will compute these Bessel functions with non-integer when «x» is non-negative. A Bessel function applied to a negative value of «x» when «n» is non-integer would result in a complex number -- in Analytica, a warning results and [[NaN]] is returned. | + | In each case, «n» is the order of the Bessel function and can be zero or greater. Analytica will compute these Bessel functions with non-integer «n» when «x» is non-negative. A Bessel function applied to a negative value of «x» when «n» is non-integer would result in a complex number -- in Analytica, a warning results and [[NaN]] is returned. |
| + | |||
| + | ''(New to [[Analytica 6.0]])'' The zeros (roots) of a Bessel function can be obtained from: | ||
| + | :<code>BesselJZero(n,k)</code> | ||
| + | :<code>BesselYzero(n,k)</code> | ||
| + | where «n» is the order and «k» is the zero number. | ||
== Library == | == Library == | ||
Advanced math | Advanced math | ||
| + | |||
| + | == Examples == | ||
| + | :<code>BesselJ(x,n)</code> →[[image:BesselJ.png]] | ||
| + | |||
| + | :<code>BesselJZero(n,k)</code> → [[image:BesselJZeros.png]] | ||
==See also== | ==See also== | ||
* [[Advanced math functions]] | * [[Advanced math functions]] | ||
* [[Complex number functions]] | * [[Complex number functions]] | ||
| + | * [[Airy functions]] | ||
Revision as of 19:13, 9 April 2021
Bessel Functions are used in engineering models to describe harmonic vibrations in cylindrical systems, such as electromagnetic waves in a cylindrical waveguide, sound vibrations in a circular membrane, or heat conduction in a cylindrical object. Analytica exposes the following Bessel functions:
BesselJ(x, n): Bessel function of the first kindBesselY(x, n): Bessel function of the second kindBesselK(x, n): Modified Bessel function of the first kindBesselY(x, n): Modified Bessel function of the second kind
In each case, «n» is the order of the Bessel function and can be zero or greater. Analytica will compute these Bessel functions with non-integer «n» when «x» is non-negative. A Bessel function applied to a negative value of «x» when «n» is non-integer would result in a complex number -- in Analytica, a warning results and NaN is returned.
(New to Analytica 6.0) The zeros (roots) of a Bessel function can be obtained from:
BesselJZero(n,k)BesselYzero(n,k)
where «n» is the order and «k» is the zero number.
Library
Advanced math
Examples
BesselJ(x,n)→
BesselJZero(n,k)→
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