Real solutions of P_III(0, 0, 4, −4) on ℝ_{> 0}

The real solutions (possibly with zeros and/or poles) of P_III(0, 0, 4, −4) on ℝ_{> 0} are by (15.10) the functions f_mult(.,s,B)|_ℝ>0 for (s, B) ∈ V^mat,ℝ. In this chapter we shall obtain complete results about the sequences of zeros and/or poles of these solutions. These global results will be derived by combining, first, the local behaviour for small x and for large x, and second, the geometry of the spaces M_3FN,ℝ^mon and M_3FN,ℝⁱⁿⁱ=M_3FN,ℝ^reg∪M_3FN,ℝ^sing, which was described in Lemma 15.4 (a) and Theorem 15.5 (a).