Difference between revisions of "Manuals/calci/BESSELI"
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<div style="font-size:30px">'''BESSELI(x,n)'''</div><br/> | <div style="font-size:30px">'''BESSELI(x,n)'''</div><br/> | ||
*<math>x</math> is the value to evaluate the function | *<math>x</math> is the value to evaluate the function | ||
− | *<math>n</math> is an integer which is the order of the Bessel function | + | *<math>n</math> is an integer which is the order of the Bessel function. |
+ | **BESSELI(), returns the modified Bessel Function In(x). | ||
+ | |||
==Description== | ==Description== | ||
*This function gives the value of the modified Bessel function. | *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 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: <math>x^2 \frac{d^2 y}{dx^2} + x\frac{dy}{dx} + (x^2 - \alpha^2)y =0</math> | + | *Bessel's Differential Equation is defined as: |
+ | <math>x^2 \frac{d^2 y}{dx^2} + x\frac{dy}{dx} + (x^2 - \alpha^2)y =0</math> | ||
where <math>\alpha</math> is the arbitrary complex number. | where <math>\alpha</math> is the arbitrary complex number. | ||
*But in most of the cases α is the non-negative real number. | *But in most of the cases α is the non-negative real number. | ||
*The solutions of this equation are called Bessel Functions of order <math>n</math>. | *The solutions of this equation are called Bessel Functions of order <math>n</math>. | ||
− | *Bessel functions of the first kind, denoted as <math> | + | *Bessel functions of the first kind, denoted as <math>J_n(x)</math>. |
− | *The <math>n^th</math> order modified Bessel function of the variable <math>x</math> is: <math> | + | *The <math>n^{th}</math> order modified Bessel function of the variable <math>x</math> is: |
− | *This function will give the result as error when 1.x or n is non | + | <math>I_n(x)=i^{-n}J_n(ix)</math>, |
+ | where : | ||
+ | <math>J_n(x)=\sum_{k=0}^\infty \frac{(-1)^k*(\frac{x}{2})^{n+2k} }{k!\Gamma(n+k+1)}</math> | ||
+ | *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. | ||
+ | |||
+ | ==ZOS== | ||
+ | *The syntax is to calculate BESSELI IN ZOS is <math>BESSELI(x,n)</math>. | ||
+ | **<math>x</math> is the value to evaluate the function | ||
+ | **<math>n</math> is an integer which is the order of the Bessel function. | ||
+ | *For e.g.,BESSELI(0.25..0.7..0.1,42) | ||
==Examples== | ==Examples== | ||
− | #BESSELI(3,2)=2.245212431 | + | #BESSELI(3,2) = 2.245212431 this is the <math>2^{nd}</math> derivative of <math>I_n(x)</math>. |
− | #BESSELI(5,1)=24.33564185 | + | #BESSELI(5,1) = 24.33564185 |
− | #BESSELI(6,0)=67.23440724 | + | #BESSELI(6,0) = 67.23440724 |
− | #BESSELI(-2,1 | + | #BESSELI(-2,1) = -1.59063685 |
− | #BESSELI(2,-1)= | + | #BESSELI(2,-1) = #N/A (ORDER OF FUNCTION < 0). |
+ | |||
+ | ==Related Videos== | ||
+ | |||
+ | {{#ev:youtube|__fdGscBZjI|280|center|BESSEL Equation}} | ||
==See Also== | ==See Also== | ||
Line 27: | Line 45: | ||
==References== | ==References== | ||
− | [http://en.wikipedia.org/wiki/Bessel_function | + | [http://en.wikipedia.org/wiki/Bessel_function Bessel Function] |
+ | |||
+ | |||
+ | |||
+ | *[[Z_API_Functions | List of Main Z Functions]] | ||
+ | |||
+ | *[[ Z3 | Z3 home ]] |
Latest revision as of 04:23, 18 November 2020
BESSELI(x,n)
- is the value to evaluate the function
- is an integer which is the order of the Bessel function.
- BESSELI(), returns the modified Bessel Function In(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:
where is the arbitrary complex number.
- But in most of the cases α is the non-negative real number.
- The solutions of this equation are called Bessel Functions of order .
- Bessel functions of the first kind, denoted as .
- The order modified Bessel function of the variable is:
, where :
- This function will give the result as error when:
1. or is non numeric 2., because is the order of the function.
ZOS
- The syntax is to calculate BESSELI IN ZOS is .
- is the value to evaluate the function
- is an integer which is the order of the Bessel function.
- For e.g.,BESSELI(0.25..0.7..0.1,42)
Examples
- BESSELI(3,2) = 2.245212431 this is the derivative of .
- BESSELI(5,1) = 24.33564185
- BESSELI(6,0) = 67.23440724
- BESSELI(-2,1) = -1.59063685
- BESSELI(2,-1) = #N/A (ORDER OF FUNCTION < 0).
Related Videos
See Also
References