diff --git a/R/fit_mvst.R b/R/fit_mvst.R
index 0c8597d..437f099 100644
--- a/R/fit_mvst.R
+++ b/R/fit_mvst.R
@@ -159,7 +159,7 @@ fit_mvst <- function(X,
     # M-step ----------------------------------------
     # nu
     if (optimize_nu) {
-      Q_nu <- function(nu) (nu/2)*sum(expect$E_logtau - log(alpha) - expect$E_tau/alpha) + T*((nu/2)*log(nu/2) - log(base::gamma(nu/2)))
+      Q_nu <- function(nu) (nu/2)*sum(expect$E_logtau - log(alpha) - expect$E_tau/alpha) + T*((nu/2)*log(nu/2) - lgamma(nu/2))
       nu <- optimize(Q_nu, interval = c(getOption("nu_min"), getOption("nu_max")), maximum = TRUE)$maximum
     }
 
@@ -351,9 +351,8 @@ besselK_ratio <- function(x, nu) {
 }
 
 
-
 log_besselK <- function(x, nu) {
-  if (nu <= 10 && nu >= -1) {
+  if (nu <= 10 && nu >= -10) {
     return(log(besselK(x, nu)))
   } else if (nu >= 0){
     nu_i <-  nu - floor(nu) + 9
@@ -384,4 +383,3 @@ log_besselK <- function(x, nu) {
     return(log_values)
   }
 }
-
diff --git a/tests/testthat/test-fit_mvst.R b/tests/testthat/test-fit_mvst.R
index 465c2d8..3b3c840 100644
--- a/tests/testthat/test-fit_mvst.R
+++ b/tests/testthat/test-fit_mvst.R
@@ -104,10 +104,38 @@ test_that("Bessel functions work", {
   res2 <- sum(dmvst(X = X, nu = 5.7, gamma = gamma, mu = mu, scatter = scatter))
   expect_equal(res1, res2)
 
+  res1 <- sum(dmvst_orig(X = X, nu = 15.7, gamma = gamma, mu = mu, scatter = scatter))
+  res2 <- sum(dmvst(X = X, nu = 15.7, gamma = gamma, mu = mu, scatter = scatter))
+  expect_equal(res1, res2)
+
   res1 <- sum(dmvst_orig(X = X, nu = 60.7, gamma = gamma, mu = mu, scatter = scatter))
   res2 <- sum(dmvst(X = X, nu = 60.7, gamma = gamma, mu = mu, scatter = scatter))
   expect_equal(res1, res2)
+  res1 <- besselK_ratio(x = 10, nu = 70)
+  res2 <- besselK(x=10, nu = 71)/besselK(x=10, nu = 70)
+  expect_equal(res1, res2)
+  res1 <- besselK_ratio(x = 0.01, nu = 5)
+  res2 <- besselK(x=0.01, nu = 6)/besselK(x=0.01, nu = 5)
+  expect_equal(res1, res2)
+  res1 <- besselK_ratio(x = 10, nu = 5)
+  res2 <- besselK(x=10, nu = 6)/besselK(x=10, nu = 5)
+  expect_equal(res1, res2)
+  res1 <- log_besselK(x = 0.01, nu = 5)
+  res2 <- log(besselK(0.01, nu = 5))
+  expect_equal(res1, res2)
+  res1 <- log_besselK(x = 0.01, nu = -5)
+  res2 <- log(besselK(0.01, nu = -5))
+  expect_equal(res1, res2)
+  res1 <- log_besselK(x = 10, nu = 5)
+  res2 <- log(besselK(10, nu = 5))
+  expect_equal(res1, res2)
+  res1 <- log_besselK(x = 10, nu = -5)
+  res2 <- log(besselK(10, nu = -5))
+  expect_equal(res1, res2)
+  res1 <- log_besselK(x = 10, nu = 70)
+  res2 <- log(besselK(10, nu = 70))
+  expect_equal(res1, res2)
+  res1 <- log_besselK(x = 10, nu = -70)
+  res2 <- log(besselK(10, nu = -70))
+  expect_equal(res1, res2)
 })
-
-
-