limited later by the fact that we cannot fit a truly infinite series to our data, and must settle for arbitrarily many terms. Table 1 shows the cumulation of our present simplifications.\
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With $2^3 = 8$ different combinations per row, we have reduced the total number of possible forms to 32. To carry out our next simplification, we make two observations. First, $\sin$ and $\cos$ differ only by a phase shift. Second, $\sinh$ can be written as a linear combination of phase-shifted $\cosh$’s. Likewise, $\cosh$ may be expressed in an analogous manner with $\sinh$’s. Thus, by introducing phase shifts $\phi_x$, $\phi_y$, and $\phi_z$ to the functions in columns 4-6 of Table 1, we may reduce the number of possible forms. As with the separation constants, in order to satisfy Maxwell’s equations, the triplet of phase shifts for $A_y$ must be the same as that for $A_z$. Furthermore, it does not matter which function in columns 4-6 of Table 1, e.g. $\sin$ or $\cos$ in the case of “Trig", we endow with the phase shift. However, anticipating the qualitative symmetry of the LGB magnetic fields to which we are fitting, it is best to make the choices presented in 