Bessel Functions
A few examples of what you can ask Wolfram|Alpha about:
Bessel Functions
plot a Bessel function
integrate a spherical Bessel function
find differential equations satisfied by a Bessel function
Airy Functions
compute a value of an Airy function to high precision
plot an Airy function
find series representations for an Airy function
find relations between functions
find differential equations satisfied by an Airy function
Struve Functions
find information about the Struve functions
Hankel Functions
generate information about the Hankel functions
compute information about the spherical Hankel functions