Expressing Functions as Sums in Mathematica: Sigma Notation Guide

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Discussion Overview

The discussion centers on how to express functions as sums in Mathematica using sigma notation, specifically focusing on the exponential function e^x and its series representation.

Discussion Character

  • Technical explanation, Conceptual clarification, Homework-related

Main Points Raised

  • One participant inquires about expressing the function e^x in sigma notation using Mathematica.
  • Another participant suggests using the Sum function in Mathematica to manually write the series.
  • A participant clarifies that they are seeking a way for Mathematica to automatically provide the sum representation for e^x.
  • Another suggestion involves using natural language input to obtain the series representation of e^x.

Areas of Agreement / Disagreement

There is no consensus on the best method to achieve the desired output in Mathematica, with multiple approaches proposed and no clear agreement on a single solution.

Contextual Notes

The discussion does not resolve the specifics of how Mathematica interprets natural language input or the limitations of the Sum function in this context.

member 428835
Does anyone know how to express a given function as a sum in mathematica using sigma notation? For example, I know how to make ##e^x = 1 + x^2/2 + x^3/6 + x^4/24...## but how would I have mathematica write it as ##e^x = \Sigma_{n=0}^{\infty} x^n/n!##?

Thanks a ton!
 
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I'm not sure what you want here. If you want to write the sum yourself, use
Code: 
Sum[x^n/(n!),{n,0,Infinity}]
Or do you want Mathematica to tell you what the sum is, given ##e^x##?
 
I was trying to have mathematica tell me the sum given ##e^x## (or any other function for that matter.

Thanks for responding!
 
The only way I can think of to obtain this is using natural language input:
Code: 
= e^x series representation
 
thanks for your help!
 

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