# Logarithmic accuracy

Does anyone know how the method of logarithmic accuracy works and what do I have to know about it (as far as applied Mathematics is concerned)? Any references, examples or guidelines would be appreciated.

Thank you

• Where have you seen it? A Google search didn't turn up anything that looked right. Apr 16 '13 at 20:51
• I have seen in a Quantum Mechanics class, in which the professor used the method to solve an integral with infrared divergence. However, I did not ask the question in the physics exchange because it appeared to be a pure mathematical question that could have been answered better by a mathematician. Apr 16 '13 at 21:05
• I am a physicist and I have no idea what you mean by "infrared divergence." Apr 16 '13 at 21:21

A quantity is said to be calculated “to logarithmic accuracy” when in an expansion like $$F(\varepsilon) = c \sum_{n=2}^{\infty} A^n \sum_{m=2}^{n} a_{n,m} \ln^{n-m}(\varepsilon/E) ~,$$ only the coefficients $a_{n,m}$ associated with the most divergent terms are calculated exactly while the coefficients for $m>2$ are determined by an approximation procedure.