Function dtaylor

• Defined in File common.h

Function Documentation

double dtaylor(int n, double alpha, double t, double prefac)

Evaluate the taylor series for r^alpha integrals.

\[ \sum_{i}t^{i}\Gamma(i+\frac{\alpha+3}{2})2^{\frac{2i}{(2i+1)!}} \]

Parameters

• n: Angular moment (the order of the derivative of the basic integral Gn in Alhrichs Phys. Chem. Chem. Phys., 8, 3072 (2006)). The maximum value implemented is n=10.
• alpha: The power of r in the potential.
• t: \( \rho|p-q|^{2} \)
• prefac: \( \frac{e^{-t}}{\rho^{\frac{3}{2}}} \) - This term helps the Taylor series to converge when t is a large number, the factor \( \frac{1}{2}\sqrt{\rho^{\alpha}} \) was “replaced” and multiplied outside, at the end, in the laplace_of_potential function.