diff --git a/CHANGELOG.md b/CHANGELOG.md
index 7d56ed1f..8b0fc679 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,7 +2,9 @@
 
 ## Unreleased
 
-+ update import in `.plotting.matplot_dep.defaults` due to change in matplotlib
+* update import in `.plotting.matplot_dep.defaults` due to change in matplotlib
+
+* Correct dl_dm term in student t inference #1065
 
 ## v1.13.1 (2024-01-14)
 
diff --git a/GPy/inference/latent_function_inference/exact_studentt_inference.py b/GPy/inference/latent_function_inference/exact_studentt_inference.py
index 161dd289..440989e1 100644
--- a/GPy/inference/latent_function_inference/exact_studentt_inference.py
+++ b/GPy/inference/latent_function_inference/exact_studentt_inference.py
@@ -35,15 +35,20 @@ class ExactStudentTInference(LatentFunctionInference):
         # Log marginal
         N = Y.shape[0]
         D = Y.shape[1]
-        log_marginal = 0.5 * (-N * np.log((nu - 2) * np.pi) - W_logdet - (nu + N) * np.log(1 + beta / (nu - 2)))
+        log_marginal = 0.5 * (
+            -N * np.log((nu - 2) * np.pi)
+            - W_logdet
+            - (nu + N) * np.log(1 + beta / (nu - 2))
+        )
         log_marginal += gammaln((nu + N) / 2) - gammaln(nu / 2)
 
         # Gradients
         dL_dK = 0.5 * ((nu + N) / (nu + beta - 2) * tdot(alpha) - D * Wi)
-        dL_dnu = -N / (nu - 2.) + digamma(0.5 * (nu + N)) - digamma(0.5 * nu)
-        dL_dnu -= np.log(1 + beta / (nu - 2.))
+        dL_dnu = -N / (nu - 2.0) + digamma(0.5 * (nu + N)) - digamma(0.5 * nu)
+        dL_dnu -= np.log(1 + beta / (nu - 2.0))
         dL_dnu += ((nu + N) * beta) / ((nu - 2) * (beta + nu - 2))
         dL_dnu *= 0.5
-        gradients = {'dL_dK': dL_dK, 'dL_dnu': dL_dnu, 'dL_dm': alpha}
+        dL_dm = (nu + N) / (nu + beta - 2) * alpha
+        gradients = {"dL_dK": dL_dK, "dL_dnu": dL_dnu, "dL_dm": dL_dm}
 
         return posterior, log_marginal, gradients