### Hypergeometric functions!

Any natural scientist or engineer would know at least one of the followings:
Hermite polynomials, Legendre polynomials, Airy function, Bessel function,
Chebyshev polynomials, Spherical harmonics, Error function, Gamma function,
Gegenbauer polynomials, and Wigner D-matrix.

For example, a biomedial engineer would know Chebyshev polynomials from
the Chebyshev filter, an electrical engineer would know Error function from
stochastic process analysis, an astronomer would know Airy function from a
diffraction analysis, a chemist would know spherical harmonics from molecular
shells, a physicists would know Legendre polynomials from quantum mechanics;
honestly, you should hesitate to call yourself a natural scientist or an engineer if
you haven’t heard any of them! (Gamma and Error functions are the ones most
likely to be known!)

Well, if you know more than one of them, then you may be surprised to learn
that all these functions, and many many more, are actually different special cases
of one big fat function: Hypergeometric function!

For a mathematician this is not that surprising; after all, all these functions
are solutions to some differential equation and hypergeometric function is simply
the solution of the more general differential equation. Still, I cherish this
knowledge, and so shall you!