Update FormalDescriptions.md

docs/funcs/FormalDescriptions.md

+# Mathematical descriptions
+
+A collection of detailed mathematical descriptions.
+
+## Index
+
+- [spikes_flagRaise](#spikes_flagraise)
+
+
+## spikes_flagRaise
+
+The value $`x_{k}`$ of a time series $`x`$ with associated 
+timestamps $`t_i`$, is flagged a rise, if:
+
+1. There is any value $`x_{s}`$, preceeding $`x_{k}`$ within `raise_window` range, so that:
+    * $` M = |x_k - x_s | > `$  `thresh` $` > 0`$ 
+2. The weighted average $`\mu^*`$ of the values, preceeding $`x_{k}`$ within `average_window` range indicates, that $`x_{k}`$ doesnt return from an outliererish value course, meaning that:  
+    * $` x_k > \mu^* + ( M `$ / `mean_raise_factor` $`)`$  
+3. Additionally, if `min_slope` is not `None`, $`x_{k}`$ is checked for being sufficiently divergent from its very predecessor $`x_{k-1}`$, meaning that, it is additionally checked if: 
+    * $`x_k - x_{k-1} > `$ `min_slope` 
+    * $`t_k - t_{k-1} > `$ `min_slope_weight`*`intended_freq`
+
+The weighted average $`\mu^*`$ was calculated with weights $`w_{i}`$, defined by: 
+* $`w_{i} = (t_i - t_{i-1})`$ / `intended_freq`, if $`(t_i - t_{i-1})`$ < `intended_freq` and $`w_i =1`$ otherwise. 
\ No newline at end of file