, certain types of entire functions
can be expressed as a certain polynomial expansion known as the Lidstone series
Let f(z) be an entire function of exponential type less than (N + 1)π, as defined below. Then f(z) can be expanded in terms of polynomials An as follows:
Here An(z) is a polynomial in z of degree n, Ck a constant, and f(n)(a) the derivative of f at a.
A function is said to be of exponential type of less than t if the function
is bounded above by t. Thus,the constant N used in the summation above is given by
- Ralph P. Boas, Jr. and C. Creighton Buck, Polynomial Expansions of Analytic Functions, (1964) Academic Press, NY. ISBN 3-540-03123-5