We present an example of algebraic elucidation of analytic expressions by the finite form of the Dirichlet class number formula. It was shown by [Hashimoto et al. (2008)] that the finite form for the Dirichlet \(L\)-function value \(L(1,χ)\), \(χ≠\chi_0\) is equivalent to Gauss’ first formula for the Euler digamma function. In this paper, we shall generalize this to the case of Discrete Fourier Transform and reveal the underlying algebraic structure.
@book{mehtakataikanemitsu,title={Chapter 18: On Periodic Dirichlet Series and Special Functions, Advanced Mathematical Analysis and its Applications (1st ed.).},author={Mehta, Jay and Kátai, Imre and Kanemitsu, S.},year={2023},publisher={Chapman and Hall/CRC},doi={https://doi.org/10.1201/9781003388678},}
