An advanced auxiliary tool for calculating the convergence domain of Dirichlet series Calculate the convergence domain and convergence radius of Dirichlet series Coefficient sequence, real part of index Convergence domain analysis, critical value, convergence judgment Peilong Formula Function Using Perron's formula for number theory calculations Sum Calculation integral calculation Asymptotic estimation Index and estimation functions Estimate the upper and lower bounds of the index sum Base, exponential coefficient, upper limit, accuracy Real part, imaginary part, modulus length, upper and lower bound estimation