Lidstone series
In mathematics, a Lidstone series, named after George James Lidstone, is a kind of polynomial expansion that can express certain types of entire functions.
Let ƒ be an entire function of exponential type less than π, as defined below. Then ƒ can be expanded in terms of polynomials An as follows:
Here An is a polynomial in z of degree n, Ck a constant, and ƒ the nth derivative of ƒ 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
with
