For a function f (x ), the series whose mth term is a_mJ₀(j_mx ), where j₁, j₂, ... are positive zeros of the Bessel function J₀ arranged in ascending order, and a_m is the product of 2/J₁² (j_m ) and the integral over t from 0 to 1 of tf (t )J₀(j_mt ); J₁ is a Bessel function.