It has been a long time since engineering school and I am not sure how to expand this series used to correct log space to arithmetic space. It is called a scale bias correction factor (SBCF). I need to expand it to 10 or 15 terms. Here it is:
In case anyone is working on this, I got an answer from another forum. It is Finneys function. The next term is: + (m-1)^7T^4/(4!m^4(n+1)(m+3)(m+5)) + ...