Mercurial > octave-antonio
diff scripts/specfun/legendre.m @ 11415:e7ed20f87e82
Add @tex blocks to gammainc and legendre docstrings.
author | Michael Godfrey <godfrey@isl.stanford.edu> |
---|---|
date | Sun, 26 Dec 2010 21:28:20 -0800 |
parents | be55736a0783 |
children | 1740012184f9 |
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--- a/scripts/specfun/legendre.m Sat Dec 25 07:47:50 2010 -0800 +++ b/scripts/specfun/legendre.m Sun Dec 26 21:28:20 2010 -0800 @@ -33,6 +33,12 @@ ## ## The Legendre Function of degree @var{n} and order @var{m}: ## +## @tex +## $$ +## P^m_n(x) = (-1)^m (1-x^2)^{m/2}{d^m\over {dx^m}}P_n (x) +## $$ +## @end tex +## @ifnottex ## @example ## @group ## m m 2 m/2 d^m @@ -40,10 +46,17 @@ ## n dx^m n ## @end group ## @end example +## @end ifnottex ## ## @noindent ## with Legendre polynomial of degree @var{n}: ## +## @tex +## $$ +## P(x) = {1\over{2^n n!}}\biggl({d^n\over{dx^n}}(x^2 - 1)^n\biggr) +## $$ +## @end tex +## @ifnottex ## @example ## @group ## 1 d^n 2 n @@ -51,6 +64,7 @@ ## n 2^n n! dx^n ## @end group ## @end example +## @end ifnottex ## ## @noindent ## @code{legendre (3, [-1.0, -0.9, -0.8])} returns the matrix: @@ -73,6 +87,12 @@ ## ## For Legendre functions of degree n and order 0: ## +## @tex +## $$ +## SP^0_n (x) = P^0_n (x) +## $$ +## @end tex +## @ifnottex ## @example ## @group ## 0 0 @@ -80,9 +100,16 @@ ## n n ## @end group ## @end example +## @end ifnottex ## ## For Legendre functions of degree n and order m: ## +## @tex +## $$ +## SP^m_n (x) = P^m_n (x)(-1)^m\biggl({2(n-m)!\over{(n+m)!}}\biggl)^{0.5} +## $$ +## @end tex +## @ifnottex ## @example ## @group ## m m m 2(n-m)! 0.5 @@ -90,6 +117,7 @@ ## n n (n+m)! ## @end group ## @end example +## @end ifnottex ## ## If the optional argument @var{normalization} is @code{"norm"}, ## compute the fully normalized associated Legendre function. @@ -98,6 +126,12 @@ ## ## For Legendre functions of degree @var{n} and order @var{m} ## +## @tex +## $$ +## NP^m_n (x) = P^m_n (x)(-1)^m\biggl({(n+0.5)(n-m)!\over{(n+m)!}}\biggl)^{0.5} +## $$ +## @end tex +## @ifnottex ## @example ## @group ## m m m (n+0.5)(n-m)! 0.5 @@ -105,6 +139,7 @@ ## n n (n+m)! ## @end group ## @end example +## @end ifnottex ## @end deftypefn ## Author: Marco Caliari <marco.caliari@univr.it>