The Real Valued J$\alpha$m Derivative

In continuation of the work presented by Pearson et al. at SESAPS 2016, we have made progress on the J$\alpha$m Derivative. Previously, we had used Wolfram Alpha to graphically analyze the derivative, but its results were incomplete. The natural logarithm of complex numbers, which occur twice in the calculations of the J$\alpha$m derivative are multivalued, with Wolfram Alpha choosing one particular value. We will present a more general case and show that a particular choice of values for these logarithms produces completely real results.