Applying this operation to the j-function led Conway and Norton to realize that certain numbers in the j function were one bigger than the number of dimensions of non-trivial representations of the group M; that realization became known as the monstrous moonshine conjecture.
Applying this operation to the j-function led Conway and Norton to realize that certain numbers in the j function were one bigger than the number of dimensions of non-trivial representations of the group M; that realization became known as the monstrous moonshine conjecture. In the context of modular forms, this function uniquely determines the modular form of functions and is sometimes named after the letter q. The integral of the square of a function f is equal to the infinite sum of the values generated by applying this function to f by Parseval's Identity. This operation applied to a function f will equal the original function if the function is (*) absolutely-integrable and contains a finite number of discontinuities as part of the Dirichlet conditions. Performing this operation on some functions, such as the square wave, leads to an undesirable "overshooting" known as the Gibbs phenomenon. For 10 points, name this operation that expresses a function as a sum of trigonometric functions.
Applying this operation to the j-function led Conway and Norton to realize that certain numbers in the j function were one bigger than the number of dimensions of non-trivial representations of the group M; that realization became known as the monstrous moonshine conjecture.
Fourier decomposition [before the letter "q" accept q-transform; accept answers indicating decomposing a function into its Fourier series; do not accept or prompt on the Fourier Transformation] 