diff --git a/docs/reference/query-languages/query-dsl/query-dsl-function-score-query.md b/docs/reference/query-languages/query-dsl/query-dsl-function-score-query.md
index b959568715406..3052c42ca6b0d 100644
--- a/docs/reference/query-languages/query-dsl/query-dsl-function-score-query.md
+++ b/docs/reference/query-languages/query-dsl/query-dsl-function-score-query.md
@@ -369,11 +369,16 @@ The `DECAY_FUNCTION` determines the shape of the decay:
 `gauss`
 :   Normal decay, computed as:
 
-![Gaussian](../images/Gaussian.png "")
 
-where ![sigma](../images/sigma.png "") is computed to assure that the score takes the value `decay` at distance `scale` from `origin`+-`offset`
+:::{math}
+S(doc) = exp \left( - \dfrac{max(0, | fieldvalue_{doc} - origin| - offset)^2)}{ 2\sigma^2 } \right)
+:::
+
+where $\sigma$ is computed to assure that the score takes the value `decay` at distance `scale` from `origin ± offset`
 
-![sigma calc](../images/sigma_calc.png "")
+:::{math}
+\sigma^2 = -scale^2 / (2 \cdot ln(decay))
+:::
 
 See [Normal decay, keyword `gauss`](#gauss-decay) for graphs demonstrating the curve generated by the `gauss` function.
 
@@ -381,11 +386,16 @@ See [Normal decay, keyword `gauss`](#gauss-decay) for graphs demonstrating the c
 `exp`
 :   Exponential decay, computed as:
 
-![Exponential](../images/Exponential.png "")
 
-where again the parameter ![lambda](../images/lambda.png "") is computed to assure that the score takes the value `decay` at distance `scale` from `origin`+-`offset`
+:::{math}
+S(doc) = exp(\lambda \cdot max(0, |fieldvalue_{doc} - origin| - offset))
+:::
 
-![lambda calc](../images/lambda_calc.png "")
+where again the parameter $\lambda$ is computed to assure that the score takes the value `decay` at distance `scale` from `origin ± offset`
+
+:::{math}
+\lambda = ln(decay)/scale
+:::
 
 See [Exponential decay, keyword `exp`](#exp-decay) for graphs demonstrating the curve generated by the `exp` function.
 
@@ -393,11 +403,16 @@ See [Exponential decay, keyword `exp`](#exp-decay) for graphs demonstrating the
 `linear`
 :   Linear decay, computed as:
 
-![Linear](../images/Linear.png "").
 
-where again the parameter `s` is computed to assure that the score takes the value `decay` at distance `scale` from `origin`+-`offset`
+:::{math}
+S(doc) = max \left( \dfrac{s - max(0, | fieldvalue_{doc} - origin| - offset)^2)}{ s }, 0 \right)
+:::
+
+where again the parameter `s` is computed to assure that the score takes the value `decay` at distance `scale` from `origin ± offset`
 
-![s calc](../images/s_calc.png "")
+:::{math}
+s = scale / (1.0 - decay)
+:::
 
 In contrast to the normal and exponential decay, this function actually sets the score to 0 if the field value exceeds twice the user given scale value.