airy
Airy functions of the first and second kind, and their derivatives.
airy(0,x) = Ai(x), airy(1,x) = Ai'(x), airy(2,x) = Bi(x), airy(3,x) = Bi'(x)
besselj
Bessel functions of the first kind.
bessely
Bessel functions of the second kind.
besseli
Modified Bessel functions of the first kind.
besselk
Modified Bessel functions of the second kind.
besselh
Compute Hankel functions of the first (k = 1) or second (k = 2) kind.
beta
The Beta function,
beta (a, b) = gamma (a) * gamma (b) / gamma (a + b).
betainc
The incomplete Beta function,
erf
The error function,
erfinv
The inverse of the error function.
gamma
The Gamma function,
gammainc
The incomplete gamma function,
For example,
sage: octave("airy(3,2)")
4.10068
sage: octave("beta(2,2)")
0.166667
sage: octave("betainc(0.2,2,2)")
0.104
sage: octave("besselh(0,2)")
(0.223891,0.510376)
sage: octave("besselh(0,1)")
(0.765198,0.088257)
sage: octave("besseli(1,2)")
1.59064
sage: octave("besselj(1,2)")
0.576725
sage: octave("besselk(1,2)")
0.139866
sage: octave("erf(0)")
0
sage: octave("erf(1)")
0.842701
sage: octave("erfinv(0.842)")
0.998315
sage: octave("gamma(1.5)")
0.886227
sage: octave("gammainc(1.5,1)")
0.77687
The Octave interface reads in even very long input (using files) in a robust manner:
sage: t = '"%s"'%10^10000 # ten thousand character string. sage: a = octave.eval(t + ';') # < 1/100th of a second sage: a = octave(t)
Note that actually reading a back out takes forever. This *must* be fixed ASAP - see http://trac.sagemath.org/sage_trac/ticket/940/.
See About this document... for information on suggesting changes.