Difference between revisions of "Manuals/calci/BESSELY"
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*The Bessel function of the second kind <math>Yn(x)</math> and sometimes it is called Weber Function or the Neumann Function.. | *The Bessel function of the second kind <math>Yn(x)</math> and sometimes it is called Weber Function or the Neumann Function.. | ||
*The Bessel function of the 2nd kind of order can be expressed as: <math>Yn(x)= \lim_{p \to n}\frac{J_p(x)Cos(p\pi)- J_{-p}(x)}{Sin(p\pi)}</math> | *The Bessel function of the 2nd kind of order can be expressed as: <math>Yn(x)= \lim_{p \to n}\frac{J_p(x)Cos(p\pi)- J_{-p}(x)}{Sin(p\pi)}</math> | ||
| − | *where Jn(x) is the Bessel functions of the first kind. | + | *where <math>Jn(x)</math> is the Bessel functions of the first kind. |
| − | *This function will give the result as error when 1.x or n is non | + | *This function will give the result as error when: |
| + | 1. <math>x</math> or <math>n</math> is non numeric | ||
| + | 2. <math>n<0</math>, because <math>n</math> is the order of the function | ||
==Examples== | ==Examples== | ||
Revision as of 23:14, 1 December 2013
BESSELY(x,n)
- 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 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
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
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
Examples
- BESSELY(2,3)=-1.127783765(EXCEL)Yn(x)=-0.1070324316(CALCI)Y1(x)
- BESSELY(0.7,4)=-132.6340573(EXCEL)Yn(x)=-1.1032498713(CALCI)Y1(x)
- BESSELY(9,1)=0.104314575
- BESSELY(2,-1)=NAN