THE BINOMIAL FUNCTION

This chapter discusses the binomial function along with the expansions in Series of Jacobi and Chebyshev polynomials, and Pade approximations. As the zeros of the Chebyshev polynomials are known, one can easily express the rational approximations as a sum of partial fractions. A certain Newton–Raphson process for finding the square root generates rational approximations of the Pade type. The chapter also discusses coefficients in the polynomials for the Pade approximations for the square and cube roots.