diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,9 @@
 # hypergeometric
 
+## 0.1.3.0
+
+  * Add `bessel1`
+
 ## 0.1.2.0
 
   * Add `tcdf`, `chisqcdf`, `fcdf`
diff --git a/hypergeometric.cabal b/hypergeometric.cabal
--- a/hypergeometric.cabal
+++ b/hypergeometric.cabal
@@ -1,6 +1,6 @@
 cabal-version:   1.18
 name:            hypergeometric
-version:         0.1.2.0
+version:         0.1.3.0
 license:         AGPL-3
 license-file:    COPYING
 copyright:       Copyright: (c) 2022 Vanessa McHale
@@ -24,8 +24,8 @@
 
 library
     exposed-modules:
-        Math.Hypergeometric
         Math.SpecialFunction
+        Math.Hypergeometric
 
     hs-source-dirs:   src
     default-language: Haskell2010
diff --git a/src/Math/SpecialFunction.hs b/src/Math/SpecialFunction.hs
--- a/src/Math/SpecialFunction.hs
+++ b/src/Math/SpecialFunction.hs
@@ -1,5 +1,6 @@
 module Math.SpecialFunction ( incbeta
                             , beta
+                            , bessel1
                             , gamma
                             , gammaln
                             , fcdf
@@ -19,6 +20,15 @@
      -> a
 tcdf 𝜈 x = 0.5 + x * gamma (0.5*(𝜈+1)) / (sqrt(pi*𝜈) * gamma(𝜈/2)) * hypergeometric [0.5, 0.5*(𝜈+1)] [1.5] (-x^(2::Int)/𝜈)
 
+-- | Bessel functions of the first kind, \( J_\alpha(x)\).
+--
+-- @since 0.1.3.0
+bessel1 :: (Floating a, Ord a)
+        => a -- ^ \(\alpha\)
+        -> a -- ^ \(x\)
+        -> a
+bessel1 𝛼 x = ((x/2)**𝛼/gamma(𝛼+1))*hypergeometric [] [𝛼+1] (-(x^(2::Int))/4)
+
 -- | @since 0.1.2.0
 {-# SPECIALIZE chisqcdf :: Double -> Double -> Double #-}
 chisqcdf :: (Floating a, Ord a)
@@ -34,7 +44,7 @@
 -- TODO: writeup?
 --
 -- chisqcdf 10 28 works better this way than w/ e^-x ... x
---
+
 -- (1 2 H. _1.1) 1 hangs indefinitely
 
 {-# SPECIALIZE incbeta :: Double -> Double -> Double -> Double #-}