diff --git a/time_series_analysis/inhom_iema.ipynb b/time_series_analysis/inhom_iema.ipynb
index 264dd3d..f3056f7 100644
--- a/time_series_analysis/inhom_iema.ipynb
+++ b/time_series_analysis/inhom_iema.ipynb
@@ -5,9 +5,29 @@
    "metadata": {},
    "source": [
     "# Iterated Exponential Moving Average on Inhomogeneous Time Series\n",
-    "This notebook calculates an Iterative Exponential Moving Average on a simulated Inhomogeneous Timer Series for 3 Values of $\\tau$ at once.\n",
+    "This notebook calculates an Iterative Exponential Moving Average on a simulated Inhomogeneous Timer Series for three rates of decay ($\\tau$) at once.\n",
     "\n",
-    "See the NAG Library for Python documentation for the further details on this function: https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.tsa.html#naginterfaces.library.tsa.inhom_iema"
+    "The `inhom_iema` routine is using a decay kernel of the following form:\n",
+    "\n",
+    "$$\n",
+    "\\frac{e^{-t_i/\\tau}}{\\tau}\n",
+    "$$\n",
+    "\n",
+    "This gives rise to the following iterative formula of the Exponential Moving Average (EMA) operator:\n",
+    "\n",
+    "$$\n",
+    "\\text{EMA}[\\tau;z](t_i)=\\mu\\text{EMA}[\\tau;z](t_{i-1})+(\\nu-\\mu)z_{i-1}+(1-\\nu)z_i\n",
+    "$$\n",
+    "\n",
+    "where $t$ is the inhomogenous (although ordered) points in time, $z$ is the set of observations, and:\n",
+    "\n",
+    "$$\n",
+    "\\mu = e^{\\alpha} \\;\\; \\text{and} \\;\\; \\alpha = \\frac{t_i - t_{i-1}}{\\tau}\n",
+    "$$\n",
+    "\n",
+    "The value of $\\nu$ depends on the method of interpolation chosen.\n",
+    "\n",
+    "See the NAG Library for Python documentation for the further details on this function: [NAG Library for Python docs](https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.tsa.html#naginterfaces.library.tsa.inhom_iema)"
    ]
   },
   {
@@ -69,7 +89,13 @@
     "\n",
     "* `tau` - the decay parameter. this script will calculate the IEMA for 3 $\\tau$ values at once\n",
     "* `sinit` -  the first two elements represent an initial point in time and a corresponding observation, while the additional elements after represent initial values for the EMA for the total number of iterations you require (e.g. if sinit has 3 elements, there will only be one iteration)\n",
-    "* `inter` - select the interpolation method for the first and subsequent iterations, respectively; see docs for more info"
+    "* `inter` - select the interpolation method for the first and subsequent iterations, respectively; see docs for more info\n",
+    "    \n",
+    "  1) Previous point:  $\\nu = 1$\n",
+    "    \n",
+    "  2) Linear:  $\\nu = (1-\\mu) / \\alpha$\n",
+    "    \n",
+    "  3) Next point:  $\\nu = \\mu$"
    ]
   },
   {