Mercurial > octave-nkf
changeset 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 | 5e6ef42a2445 |
| children | 74e285bb61c9 |
| files | scripts/ChangeLog scripts/specfun/legendre.m src/ChangeLog src/DLD-FUNCTIONS/gammainc.cc |
| diffstat | 4 files changed, 53 insertions(+), 10 deletions(-) [+] |
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--- a/scripts/ChangeLog Sat Dec 25 07:47:50 2010 -0800 +++ b/scripts/ChangeLog Sun Dec 26 21:28:20 2010 -0800 @@ -1,3 +1,7 @@ +2010-12-26 Michael Godfrey <godfrey@isl.stanford.edu> + + * specfun/legendre.m: Add @tex blocks to docstring. + 2010-12-24 Rik <octave@nomad.inbox5.com> * testfun/test.m: Use 'Command' for deftype in docstring.
--- 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>
--- a/src/ChangeLog Sat Dec 25 07:47:50 2010 -0800 +++ b/src/ChangeLog Sun Dec 26 21:28:20 2010 -0800 @@ -1,3 +1,7 @@ +2010-12-26 Michael Godfrey <godfrey@isl.stanford.edu> + + * gammainc.cc: Add @tex blocks to docstring. + 2010-12-25 Rik <octave@nomad.inbox5.com> * DLD-FUNCTIONS/str2double.cc: Fix bug in converting "numberi" strings
--- a/src/DLD-FUNCTIONS/gammainc.cc Sat Dec 25 07:47:50 2010 -0800 +++ b/src/DLD-FUNCTIONS/gammainc.cc Sun Dec 26 21:28:20 2010 -0800 @@ -41,20 +41,20 @@ Compute the normalized incomplete gamma function,\n\ @tex\n\ $$\n\ - \\gamma (x, a) = {\\displaystyle\\int_0^x e^{-t} t^{a-1} dt \\over \\Gamma (a)}\n\ + \\gamma (x, a) = {1 \\over {\\Gamma (a)}}\\displaystyle{\\int_0^x t^{a-1} e^{-t} dt}\n\ $$\n\ @end tex\n\ @ifnottex\n\ \n\ -@smallexample\n\ +@example\n\ @group\n\ - x\n\ - 1 /\n\ + x\n\ + 1 /\n\ gammainc (x, a) = --------- | exp (-t) t^(a-1) dt\n\ - gamma (a) /\n\ - t=0\n\ + gamma (a) /\n\ + t=0\n\ @end group\n\ -@end smallexample\n\ +@end example\n\ \n\ @end ifnottex\n\ with the limiting value of 1 as @var{x} approaches infinity.\n\ @@ -64,14 +64,14 @@ for each element of @var{x} and vice versa.\n\ \n\ If neither @var{x} nor @var{a} is scalar, the sizes of @var{x} and\n\ -@var{a} must agree, and @var{gammainc} is applied element-by-element.\n\ +@var{a} must agree, and @code{gammainc} is applied element-by-element.\n\ \n\ By default the incomplete gamma function integrated from 0 to @var{x} is\n\ computed. If \"upper\" is given then the complementary function integrated\n\ -for @var{x} to infinity is calculated. It should be noted that\n\ +from @var{x} to infinity is calculated. It should be noted that\n\ \n\ @example\n\ -gammainc (@var{x}, @var{a}) = 1 - gammainc (@var{x}, @var{a}, \"upper\")\n\ +gammainc (@var{x}, @var{a}) @equiv{} 1 - gammainc (@var{x}, @var{a}, \"upper\")\n\ @end example\n\ @seealso{gamma, lgamma}\n\ @end deftypefn")