From d9587127d59627924871e740675fe4245b3637e2 Mon Sep 17 00:00:00 2001
From: Ferrangelo <85937147+Ferrangelo@users.noreply.github.com>
Date: Sun, 17 Aug 2025 12:11:22 +0200
Subject: [PATCH] Correct implementation of spherical bessel functions (#992)

Closes #991
---
 mpmath/functions/bessel.py      | 4 ++--
 mpmath/tests/test_functions2.py | 4 ++++
 2 files changed, 6 insertions(+), 2 deletions(-)

diff --git a/mpmath/functions/bessel.py b/mpmath/functions/bessel.py
index 42b7f208..d8fe37ca 100644
--- a/mpmath/functions/bessel.py
+++ b/mpmath/functions/bessel.py
@@ -218,7 +218,7 @@ def spherical_jn(ctx, n, z):
     mpf('0.84147098480789639')
 
     """
-    return ctx.besselj(n + ctx.one/2, z) * ctx.sqrt(ctx.pi/2*z)
+    return ctx.besselj(n + ctx.one/2, z) * ctx.sqrt(ctx.pi/(2*z))
 
 @defun
 def spherical_yn(ctx, n, z):
@@ -240,7 +240,7 @@ def spherical_yn(ctx, n, z):
     mpf('-0.54030230586813965')
 
     """
-    return ctx.bessely(n + ctx.one/2, z) * ctx.sqrt(ctx.pi/2*z)
+    return ctx.bessely(n + ctx.one/2, z) * ctx.sqrt(ctx.pi/(2*z))
 
 @defun_wrapped
 def whitm(ctx,k,m,z,**kwargs):
diff --git a/mpmath/tests/test_functions2.py b/mpmath/tests/test_functions2.py
index 0392ecba..cd925c8a 100644
--- a/mpmath/tests/test_functions2.py
+++ b/mpmath/tests/test_functions2.py
@@ -2454,3 +2454,7 @@ def test_issue_908():
 def test_issue_637():
     assert hankel1(1, 1 + 30j).ae(-7.25495e-15 - 1.17346e-14j)
     assert hankel2(1, 1 - 30j).ae(-7.25495e-15 + 1.17346e-14j)
+
+def test_issue_991():
+    assert spherical_jn(0, 1.3).ae(0.74119860416707)
+    assert spherical_yn(0, 1.3).ae(-0.20576832971122)