chore: update papers, add assumptions in 'Sum Analysis' paper.

Signed-off-by: Amlal El Mahrouss <amlal@nekernel.org>

1 files changed, 2 insertions, 2 deletions

diff --git a/source/wg04/paper.2.tex b/source/wg04/paper.2.tex
index 52ddb66..0cbfd64 100644
--- a/source/wg04/paper.2.tex
+++ b/source/wg04/paper.2.tex
@@ -28,11 +28,11 @@ We assume $x \in \mathbb{R}, \quad a, b \in \mathbb{N}, \quad 0 < a < b < \cos(0
 
 \subsection{The S-Integral:}
 \begin{equation}
-    I_{1} \coloneqq \int_{a}^{b} S(x)dx, \quad \forall a, b \in \mathbb{R}, \quad 0 < a < b
+    I_{1} \coloneqq \int_{a}^{b} S(x)dx
 \end{equation}
 \subsection{The S-Function:}
 \begin{equation}
-    S(x) := x^{e}, \quad x \in \mathbb{R}, \quad x > 0
+    S(x) = \sum_{k=1}^{t} (\frac{dx}{du}) \cdot x, \quad x > 0, \quad t > k
 \end{equation}
 
 \end{document}