Difference between revisions of "Manuals/calci/BESSELY"
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*<math>x</math> is the value at which to evaluate the function | *<math>x</math> is the value at which to evaluate the function | ||
*<math>n</math> is the integer which is the order of the Bessel Function | *<math>n</math> is the integer which is the order of the Bessel Function | ||
| − | + | **BESSELY(), returns the Bessel Function Yn(x) | |
==Description== | ==Description== | ||
*This function gives the value of the modified Bessel function. | *This function gives the value of the modified Bessel function. | ||
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2. <math>n<0</math>, because <math>n</math> is the order of the function. | 2. <math>n<0</math>, because <math>n</math> is the order of the function. | ||
| − | ==ZOS | + | ==ZOS== |
*The syntax is to calculate BESSELY in ZOS is <math>BESSELY(x,n)</math>. | *The syntax is to calculate BESSELY in ZOS is <math>BESSELY(x,n)</math>. | ||
**<math>x</math> is the value at which to evaluate the function | **<math>x</math> is the value at which to evaluate the function | ||
**<math>n</math> is the integer which is the order of the Bessel Function | **<math>n</math> is the integer which is the order of the Bessel Function | ||
| + | ==Examples== | ||
| + | |||
| + | #=BESSELY(2,3) = -1.1277837651220644 | ||
| + | #=BESSELY(0.7,4)= -132.6340573047033 | ||
| + | #=BESSELY(9,1) = 0.10431457495919716 | ||
| + | #=BESSELY(2,-1) = #N/A (ORDER OF FUNCTION < 0) | ||
| − | == | + | ==Related Videos== |
| − | # | + | {{#ev:youtube|__fdGscBZjI|280|center|BESSEL Equation}} |
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==See Also== | ==See Also== | ||
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==References== | ==References== | ||
[http://en.wikipedia.org/wiki/Bessel_function Bessel Function] | [http://en.wikipedia.org/wiki/Bessel_function Bessel Function] | ||
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| + | |||
| + | |||
| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | |||
| + | *[[ Z3 | Z3 home ]] | ||
Latest revision as of 07:07, 29 September 2021
BESSELY(x,n)
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} is the value at which to evaluate the function
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n}
is the integer which is the order of the Bessel Function
- BESSELY(), returns the Bessel Function Yn(x)
Description
- This function gives the value of the modified Bessel function.
- Bessel functions is also called Cylinder Functions because they appear in the solution to Laplace's equation in cylindrical coordinates.
- Bessel's Differential Equation is defined as: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2 \frac{d^2 y}{dx^2} + x\frac{dy}{dx} + (x^2 - \alpha^2)y =0}
where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha} is the arbitrary complex number.
- But in most of the cases Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha} is the non-negative real number.
- The solutions of this equation are called Bessel Functions of order Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} .
- The Bessel function of the second kind Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Yn(x)} and sometimes it is called Weber Function or the Neumann Function..
- The Bessel function of the 2nd kind of order can be expressed as: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Yn(x)= \lim_{p \to n}\frac{J_p(x)Cos(p\pi)- J_{-p}(x)}{Sin(p\pi)}}
- where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Jn(x)} is the Bessel functions of the first kind.
- This function will give the result as error when:
1. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x}
or is non numeric
2. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n<0}
, because Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n}
is the order of the function.
ZOS
- The syntax is to calculate BESSELY in ZOS is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle BESSELY(x,n)}
.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} is the value at which to evaluate the function
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} is the integer which is the order of the Bessel Function
Examples
- =BESSELY(2,3) = -1.1277837651220644
- =BESSELY(0.7,4)= -132.6340573047033
- =BESSELY(9,1) = 0.10431457495919716
- =BESSELY(2,-1) = #N/A (ORDER OF FUNCTION < 0)
Related Videos
See Also
References