Better doc for jax.numpy.i0

jax/_src/numpy/lax_numpy.py

@@ -5973,19 +5973,53 @@ def meshgrid(*xi: ArrayLike, copy: bool = True, sparse: bool = False,
   return output
 
 
-@custom_jvp
-@util.implements(np.i0)
 @jit
 def i0(x: ArrayLike) -> Array:
+  r"""Calculate modified Bessel function of first kind, zeroth order.
+
+  JAX implementation of :func:`numpy.i0`.
+
+  Modified Bessel function of first kind, zeroth order is defined by:
+
+  .. math::
+
+     \mathrm{i0}(x) = I_0(x) = \sum_{k=0}^{\infty} \frac{(x^2/4)^k}{(k!)^2}
+
+  Args:
+    x: scalar or array. Specifies the argument of Bessel function. Complex inputs
+      are not supported.
+
+  Returns:
+    An array containing the corresponding vlaues of the modified Bessel function
+    of ``x``.
+
+  See also:
+    - :func:`jax.scipy.special.i0`: Calculates the modified Bessel function of
+      zeroth order.
+    - :func:`jax.scipy.special.i1`: Calculates the modified Bessel function of
+      first order.
+    - :func:`jax.scipy.special.i0e`: Calculates the exponentially scaled modified
+      Bessel function of zeroth order.
+
+  Examples:
+    >>> x = jnp.array([-2, -1, 0, 1, 2])
+    >>> jnp.i0(x)
+    Array([2.2795851, 1.266066 , 1.0000001, 1.266066 , 2.2795851], dtype=float32)
+  """
   x_arr, = util.promote_args_inexact("i0", x)
   if not issubdtype(x_arr.dtype, np.floating):
     raise ValueError(f"Unsupported input type to jax.numpy.i0: {_dtype(x)}")
-  x_arr = lax.abs(x_arr)
-  return lax.mul(lax.exp(x_arr), lax.bessel_i0e(x_arr))
+  return _i0(x_arr)
+
+
+@custom_jvp
+def _i0(x):
+  abs_x = lax.abs(x)
+  return lax.mul(lax.exp(abs_x), lax.bessel_i0e(abs_x))
 
-@i0.defjvp
+@_i0.defjvp
 def _i0_jvp(primals, tangents):
-  primal_out, tangent_out = jax.jvp(i0.fun, primals, tangents)
+  primal_out, tangent_out = jax.jvp(_i0.fun, primals, tangents)
   return primal_out, where(primals[0] == 0, 0.0, tangent_out)
 
 def ix_(*args: ArrayLike) -> tuple[Array, ...]: