From b3ba786d9ba12b76d0b14325ca3fea569eb5210b Mon Sep 17 00:00:00 2001 From: TaralMunot <125088315+TaralMunot@users.noreply.github.com> Date: Sun, 12 Feb 2023 15:25:18 +0530 Subject: [PATCH 1/4] Delete me22b160.tex --- me22b160.tex | 0 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 me22b160.tex diff --git a/me22b160.tex b/me22b160.tex deleted file mode 100644 index e69de29..0000000 From 9ad3efd4dc669b126d1b9a1d80bc150e21ffae17 Mon Sep 17 00:00:00 2001 From: TaralMunot <125088315+TaralMunot@users.noreply.github.com> Date: Sun, 12 Feb 2023 15:26:04 +0530 Subject: [PATCH 2/4] Added ME22B160 --- me22b160.tex | 15 +++++++++++++++ 1 file changed, 15 insertions(+) create mode 100644 me22b160.tex diff --git a/me22b160.tex b/me22b160.tex new file mode 100644 index 0000000..93a4abf --- /dev/null +++ b/me22b160.tex @@ -0,0 +1,15 @@ +\section{ME22B160} +\subsection{A very interesting summation given by Euler} +\begin{equation} + e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} +\end{equation} +\subsection{Introduction} +This is a summation which transforms the power function of e into a beautiful summation. + +Euler must have been a real genius to discover such a number. The number itself is a really interesting one. For more information, refer to this video of Numberphile. \footnote{\href{https://www.youtube.com/watch?v=AuA2EAgAegE}{Numberphile's video on Euler's Number}} +\subsection{Uses of the exponential function} +The sum has much more use over the number itself. Some hyperbolic functions are the literal transformation derived from this summation itself. Another intersting use of this summation is in the fields of complex numbers and Binomial Theorem. Refer to the wikipedia link for more information on this. \footnote{\href{https://en.wikipedia.org/wiki/Exponential_function}{Wikipedia link}} +\begin{itemize} + \item Use in BT:- Some complex bino-binomial sums are calculated using power functions and consequently, power sum of euler's number. + \item Use in Complex Numbers:- Euler's form of complex numbers is somewhat derived from this expression. +\end{itemize} \ No newline at end of file From 047f95087845e6ac2602db96e9e6fe6797d81c0b Mon Sep 17 00:00:00 2001 From: TaralMunot <125088315+TaralMunot@users.noreply.github.com> Date: Sun, 12 Feb 2023 15:50:18 +0530 Subject: [PATCH 3/4] Delete me22b160.tex --- me22b160.tex | 15 --------------- 1 file changed, 15 deletions(-) delete mode 100644 me22b160.tex diff --git a/me22b160.tex b/me22b160.tex deleted file mode 100644 index 93a4abf..0000000 --- a/me22b160.tex +++ /dev/null @@ -1,15 +0,0 @@ -\section{ME22B160} -\subsection{A very interesting summation given by Euler} -\begin{equation} - e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} -\end{equation} -\subsection{Introduction} -This is a summation which transforms the power function of e into a beautiful summation. - -Euler must have been a real genius to discover such a number. The number itself is a really interesting one. For more information, refer to this video of Numberphile. \footnote{\href{https://www.youtube.com/watch?v=AuA2EAgAegE}{Numberphile's video on Euler's Number}} -\subsection{Uses of the exponential function} -The sum has much more use over the number itself. Some hyperbolic functions are the literal transformation derived from this summation itself. Another intersting use of this summation is in the fields of complex numbers and Binomial Theorem. Refer to the wikipedia link for more information on this. \footnote{\href{https://en.wikipedia.org/wiki/Exponential_function}{Wikipedia link}} -\begin{itemize} - \item Use in BT:- Some complex bino-binomial sums are calculated using power functions and consequently, power sum of euler's number. - \item Use in Complex Numbers:- Euler's form of complex numbers is somewhat derived from this expression. -\end{itemize} \ No newline at end of file From b3adaf14856e0c83073e36d3818d6c9fc53d1f6c Mon Sep 17 00:00:00 2001 From: TaralMunot <125088315+TaralMunot@users.noreply.github.com> Date: Sun, 12 Feb 2023 15:50:48 +0530 Subject: [PATCH 4/4] Update ME22B160 --- me22b160.tex | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) create mode 100644 me22b160.tex diff --git a/me22b160.tex b/me22b160.tex new file mode 100644 index 0000000..cc7dbf0 --- /dev/null +++ b/me22b160.tex @@ -0,0 +1,17 @@ +\section{ME22B160} +\subsection{A very interesting summation given by Euler} +\begin{equation} + e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} +\end{equation} +\subsection{Introduction} +This is a summation which transforms the power function of e into a beautiful summation. + +Euler must have been a real genius to discover such a number. The number itself is a really interesting one. For more information, refer to this video of Numberphile. \footnote{\href{https://www.youtube.com/watch?v=AuA2EAgAegE}{Numberphile's video on Euler's Number}} +\subsection{Uses of the exponential function} +The sum has much more use over the number itself. Some hyperbolic functions are the literal transformation derived from this summation itself. Another intersting use of this summation is in the fields of complex numbers and Binomial Theorem. Refer to the wikipedia link for more information on this. \footnote{\href{https://en.wikipedia.org/wiki/Exponential_function}{Wikipedia link}} +\begin{itemize} + \item Use in BT:- Some complex bino-binomial sums are calculated using power functions and consequently, power sum of euler's number. + \item Use in Complex Numbers:- Euler's form of complex numbers is somewhat derived from this expression. +\end{itemize} + +Name- Taral Munot | Roll number- ME22B160 | GitHub user ID- TaralMunot \ No newline at end of file