This book is mainly about four functions denoted by r, R, S, and 2 F 0 . The first is the gamma function, Euler's extension of the factorial function 11! to nonintegral values of 11 . The other three are hypergeometric functions and embrace as special cases the functions named after Bessel, Hankel, Legendre, Gauss, Kummer, Whittaker, Jacobi, Chebyshev, Gegenbauer, Laguerre, Hermite, and others. The R function unites Gauss's hypergeometric function with the elliptic integrals and the first Appell function.