# HG changeset patch
# User Michael Godfrey <address@hidden>
# Date 1292974675 28800
# Node ID 7c7091ffe08e3a13b9078b021c8b0b81f90e7bc8
# Parent  36dbe5124d21237abdbd095642344e723eff4365
update doc gammainc and legendre

diff -r 36dbe5124d21 -r 7c7091ffe08e scripts/specfun/legendre.m
--- a/scripts/specfun/legendre.m	Mon Dec 20 14:59:41 2010 -0800
+++ b/scripts/specfun/legendre.m	Tue Dec 21 15:37:55 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 <address@hidden>
diff -r 36dbe5124d21 -r 7c7091ffe08e src/DLD-FUNCTIONS/gammainc.cc
--- a/src/DLD-FUNCTIONS/gammainc.cc	Mon Dec 20 14:59:41 2010 -0800
+++ b/src/DLD-FUNCTIONS/gammainc.cc	Tue Dec 21 15:37:55 2010 -0800
@@ -41,7 +41,7 @@
 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\