 formula_74, "i" = 0, 1, 2, ...) the ending point will be on an incongruity as well, by equation (17) (since formula_3 is an integer and formula_5 is an integer, formula_33 will be an integer).In this case, we can achieve this same index (difference in positive and negative jumps) by shifting the axes of the tangent function by formula_78, through adding formula_78 to formula_37.Thus, our index is now fully defined for any combination of coefficients in formula_8 by evaluating formula_82 over the interval (a,b) = formula_83 when our starting (and thus ending) point is not an incongruity, and by evaluating
over said interval when our starting point is at an incongruity.