Special Functions
A few examples of what you can ask Wolfram|Alpha about:
compute properties of the Gamma function
simplify expressions involving Gamma
Beta Functions
compute values of the Beta function
plot values of the incomplete Beta function
Error Functions
compute values of the error function
analyze the complementary error function
plot a Bessel function
integrate a spherical Bessel function
Legendre Polynomials
compute Legendre P polynomials
plot a Legendre Q polynomial
plot an elliptic integral
compute the Taylor series of nome
plot the zeta function on the critical line
numerically evaluate zeta near one of the nontrivial zeros
Spheroidal Functions
evaluate S1 numerically