Schlömilch's series is a Fourier series type expansion of twice continuously differentiable function in the interval
( 0 , π )
in terms of the Bessel function of the first kind, named after the German mathematician Oskar Schlömilch, who derived the series in 1857.
[1][2][3][4][5] The real-valued function
has the following expansion: where Some examples of Schlömilch's series are the following: