From f9251dc271aa59ce489359ad27b6abed20be613f Mon Sep 17 00:00:00 2001
From: Marco Berzborn <m.berzborn@tue.nl>
Date: Tue, 18 Nov 2025 17:49:00 +0100
Subject: [PATCH] Make the starting element in assoc_legendre_p_pm1 depend on
 the sign of z

---
 include/xsf/legendre.h | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/include/xsf/legendre.h b/include/xsf/legendre.h
index 23fb9e8f3..f9aa9d642 100644
--- a/include/xsf/legendre.h
+++ b/include/xsf/legendre.h
@@ -310,7 +310,11 @@ void assoc_legendre_p_pm1(NormPolicy norm, int n, int m, T z, int branch_cut, T
 template <typename NormPolicy, typename T, size_t Order>
 void assoc_legendre_p_pm1(NormPolicy norm, int n, int m, dual<T, Order> z, int branch_cut, dual<T, Order> &res) {
     if (m == 0) {
-        res[0] = T(1);
+        if (real(z[0]) >= 0) {
+            res[0] = T(1);
+        } else {
+            res[0] = T(-1);
+        }
     } else {
         res[0] = T(0);
     }