Schlömilch's Series
A Fourier Series-like expansion of a twice continuously differentiable function
for
, where 
is a zeroth order Bessel Function of the First Kind and |  |  | |
 | |  |
A special case gives the amazing identity
See also Bessel Function of the First Kind, Bessel Function Fourier Expansion,Fourier Series
References
Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1473, 1980.
- Gaussian Coordinate System
- Gaussian Curvature
- Gaussian Differential Equation
- Gaussian Distribution
- Gaussian Distribution Linear Combination of Variates
- Gaussian Elimination
- Gaussian Function
- Gaussian Hypergeometric Series
- Gaussian Integer
- Gaussian Integral
- Gaussian Integral (Linking Number)
- Gaussian Joint Variable Theorem
- Gaussian Mountain Range
- Gaussian Multivariate Distribution
- Gaussian Polynomial
- Gaussian Prime
- Gaussian Quadrature
- Gaussian Sum
- Gauss-Jacobi Mechanical Quadrature
- Gauss-Jordan Elimination
- Gauss-Kummer Series
- Gauss-Kuzmin-Wirsing Constant
- Gauss-Laguerre Quadrature
- Gauss-Manin Connection
- Gauss Map