Holonomic function

Summary

A holonomic function, also called a D-finite function, is a function or formal power series that satisfies a linear differential equation whose coefficients are polynomials. Many special functions are holonomic, for example the exponential, the sine, the logarithm, the hypergeometric function and the Bessel functions. The class is closed under sums and products, and the coefficients of a holonomic power series satisfy a recurrence with polynomial coefficients. For this reason such a differential equation is a finite data structure for the function, which computer algebra uses to prove identities automatically.