Summation of exponentials, as a multiplication of exponentials?

Click For Summary

Discussion Overview

The discussion centers around the mathematical relationship between the summation of exponential functions and their multiplication. Participants explore whether a summation of exponentials can be expressed as a product of exponentials, examining the validity of various expressions and identities.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant states that while the multiplication of exponentials follows the rule e^a e^b = e^{a + b}, there is no analogous rule for summation, specifically e^a + e^b ≠ e^{a b}.
  • Another participant suggests a transformation of the summation, proposing that e^a + e^b can be rewritten as e^a * (1 + e^(b-a)).
  • A third participant expresses agreement with the previous statements without introducing new claims.

Areas of Agreement / Disagreement

Participants generally agree on the lack of a direct equivalence between the summation and multiplication of exponentials, but they propose different forms and transformations related to the summation.

Contextual Notes

The discussion does not resolve the broader implications or applications of these transformations, nor does it address any assumptions underlying the proposed expressions.

EngWiPy
Messages
1,361
Reaction score
61
Hello,

Can we write a summation of exponentials, as a multiplication of exponentials?

Regards
 
Mathematics news on Phys.org


Only like
[tex]e^a e^b = e^{a + b}[/tex]

There is no such rule as
[tex]e^a + e^b = e^{a b}[/tex]
or something like that.
 


Best I can do is e^a + e^b = e^a * (1 + e^(b-a)).
 


Yes I agree with both of you. Thank you
 

Similar threads

Undergrad Polynomial vs. Exponential time
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad P-adic numbers and the Ramanujan summation
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad Can I Use a Natural Log Function for Least Square Fitting?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Exponential of hypercomplex numbers
  • · Replies 3 ·
Replies
3
Views
2K
Graduate What does the exponential term mean in Fourier transform
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Predict Digits of Irrational Numbers with Modular Arithmetic Summation?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Summation for extended binomial coefficients
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Method for finding a complex series?
  • · Replies 10 ·
Replies
10
Views
3K
MHB How can I solve more complex exponential equations?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad How can I go from sine to cosine using exponential numbers?
  • · Replies 3 ·
Replies
3
Views
2K