Jacobi poly: Difference between revisions
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Created page with "{{Function |name=jacobi_poly |desc=Computes the coefficients of Jacobi polynomials |upd=March 6, 2013 |v=1.00 |helper=1}} <tt>'''jacobi_poly'''</tt> is a [[List of functions|f..." |
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|name=jacobi_poly | |name=jacobi_poly | ||
|desc=Computes the coefficients of Jacobi polynomials | |desc=Computes the coefficients of Jacobi polynomials | ||
|cat=[[List of functions#Helper_functions|Helper functions]] | |||
|upd=March 6, 2013 | |upd=March 6, 2013 | ||
|v= | |v=0.50 | ||
|helper=1}} | |helper=1}} | ||
<tt>'''jacobi_poly'''</tt> is a [[List of functions|function]] that returns a vector containing the coefficients of the specified [http://en.wikipedia.org/wiki/Jacobi_polynomials Jacobi polynomial]. | <tt>'''jacobi_poly'''</tt> is a [[List of functions|function]] that returns a vector containing the coefficients of the specified [http://en.wikipedia.org/wiki/Jacobi_polynomials Jacobi polynomial]. | ||
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==Examples== | ==Examples== | ||
The Jacobi polynomials are typically denoted by the notation <math>P^{(\alpha,\beta)}_n</math>. In the <math>\alpha = \beta = 1, n = 3</math> case, we have <math>P^{(1,1)}_3(z) = 7z^3 - 3z</math>, which we can see via the following code: | The Jacobi polynomials are typically denoted by the notation <math>P^{(\alpha,\beta)}_n</math>. In the <math>\alpha = \beta = 1, n = 3</math> case, we have <math>P^{(1,1)}_3(z) = 7z^3 - 3z</math>, which we can see via the following code: | ||
< | <syntaxhighlight> | ||
>> jacobi_poly(1,1,3) | >> jacobi_poly(1,1,3) | ||
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7 0 -3 0 | 7 0 -3 0 | ||
</ | </syntaxhighlight> | ||
{{SourceCode|name=jacobi_poly|helper=1}} | |||
Latest revision as of 15:59, 29 September 2014
| jacobi_poly | |
| Computes the coefficients of Jacobi polynomials | |
| Other toolboxes required | none |
|---|---|
| Function category | Helper functions |
| This is a helper function that only exists to aid other functions in QETLAB. If you are an end-user of QETLAB, you likely will never have a reason to use this function. |
jacobi_poly is a function that returns a vector containing the coefficients of the specified Jacobi polynomial.
Syntax
- JP = jacobi_poly(A,B,N)
Argument descriptions
- A: A real parameter (sometimes called alpha) of the Jacobi polynomials.
- B: A real parameter (sometimes called beta) of the Jacobi polynomials.
- N: The degree of the Jacobi polynomial (a non-negative integer).
Examples
The Jacobi polynomials are typically denoted by the notation <math>P^{(\alpha,\beta)}_n</math>. In the <math>\alpha = \beta = 1, n = 3</math> case, we have <math>P^{(1,1)}_3(z) = 7z^3 - 3z</math>, which we can see via the following code:
>> jacobi_poly(1,1,3)
ans =
7 0 -3 0Source code
Click here to view this function's source code on github.