X-Git-Url: http://gitweb.michael.orlitzky.com/?p=octave.git;a=blobdiff_plain;f=legendre_p.m;fp=legendre_p.m;h=6238929eb2e4aea13ea1cc1548b82dcc59fdb301;hp=0000000000000000000000000000000000000000;hb=ee06b882dfb9a86788d7057cec8ca6d7680c5ca5;hpb=2fbcf94908d646ec62d2f15f7ec35288c6ac1cfe

diff --git a/legendre_p.m b/legendre_p.m
new file mode 100644
index 0000000..6238929
--- /dev/null
+++ b/legendre_p.m
@@ -0,0 +1,27 @@
+function P = legendre_p(n)
+  ## Return the nth legendre polynomial.
+  ##
+  ## INPUTS:
+  ##
+  ##   * ``n`` - The index of the polynomial that we want.
+  ##
+  ## OUTPUTS:
+  ##
+  ##   * ``P`` - A polynomial function of one argument.
+  ##
+  if (n < 0)
+    ## Can't do anything here. Return nothing.
+    P = NA;
+  elseif (n == 0)
+    ## One of our base cases.
+    P = @(x) 1
+  elseif (n == 1)
+    ## The second base case.
+    P = @(x) x
+  else
+    ## Compute recursively.
+    prev = legendre_p(n-1)
+    prev_prev = legendre_p(n-2)
+    P = @(x) (1/n)*( (2*n - 1)*prev(x) - (n-1)*prev_prev(x) )
+  end
+end