Dgdrxrt

What is the largest species of polychaete?

Need a suitable toxic chemical for a murder plot in my novel

What was the last x86 CPU that did not have the x87 floating-point unit built in?

What's the point in a preamp?

Unexpected result with right shift after bitwise negation

Replacing HDD with SSD; what about non-APFS/APFS?

Determine whether f is a function, an injection, a surjection

How can players take actions together that are impossible otherwise?

Was credit for the black hole image misattributed?

Geometric mean and geometric standard deviation

What would be Julian Assange's expected punishment, on the current English criminal law?

Blender game recording at the wrong time

If A makes B more likely then B makes A more likely"

How to market an anarchic city as a tourism spot to people living in civilized areas?

Jazz greats knew nothing of modes. Why are they used to improvise on standards?

How do you clear the ApexPages.getMessages() collection in a test?

Problem when applying foreach loop

When communicating altitude with a '9' in it, should it be pronounced "nine hundred" or "niner hundred"?

Area of a 2D convex hull

What items from the Roman-age tech-level could be used to deter all creatures from entering a small area?

If I can make up priors, why can't I make up posteriors?

Should you tell Jews they are breaking a commandment?

New Order #5: where Fibonacci and Beatty meet at Wythoff

What did Darwin mean by 'squib' here?

Is the integral of $x^x^x^.^…$ defined only from 0 to $x=e^frac1e$? [on hold]

0

$begingroup$

As seen in the graph of $ y = x^y $ https://www.desmos.com/calculator/we9o01ewit, x starts decreasing after $x=e^frac1e$

So is the integral of $x^x^x^.^.......$ defined only from 0 to $x=e^frac1e$?

calculus integration definite-integrals

share|cite|improve this question

asked Mar 31 at 19:19

Rithik KapoorRithik Kapoor

39510

$endgroup$

put on hold as off-topic by Saad, Shaun, GNUSupporter 8964民主女神 地下教會, José Carlos Santos, Juniven Apr 10 at 23:22

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Shaun, GNUSupporter 8964民主女神 地下教會, José Carlos Santos, Juniven

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Please don't use frac in exponents or limits of integrals. It looks bad and confusing, and it rarely appears in professional mathematics typesetting.
  $endgroup$
  – GNUSupporter 8964民主女神 地下教會
  Apr 10 at 11:08
  

  
  
  
  

add a comment | 

0

$begingroup$

As seen in the graph of $ y = x^y $ https://www.desmos.com/calculator/we9o01ewit, x starts decreasing after $x=e^frac1e$

So is the integral of $x^x^x^.^.......$ defined only from 0 to $x=e^frac1e$?

calculus integration definite-integrals

share|cite|improve this question

asked Mar 31 at 19:19

Rithik KapoorRithik Kapoor

39510

$endgroup$

put on hold as off-topic by Saad, Shaun, GNUSupporter 8964民主女神 地下教會, José Carlos Santos, Juniven Apr 10 at 23:22

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, Shaun, GNUSupporter 8964民主女神 地下教會, José Carlos Santos, Juniven

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Please don't use frac in exponents or limits of integrals. It looks bad and confusing, and it rarely appears in professional mathematics typesetting.
  $endgroup$
  – GNUSupporter 8964民主女神 地下教會
  Apr 10 at 11:08
  

  
  
  
  

add a comment | 

$begingroup$

As seen in the graph of $ y = x^y $ https://www.desmos.com/calculator/we9o01ewit, x starts decreasing after $x=e^frac1e$

So is the integral of $x^x^x^.^.......$ defined only from 0 to $x=e^frac1e$?

calculus integration definite-integrals

share|cite|improve this question

asked Mar 31 at 19:19

Rithik KapoorRithik Kapoor

39510

$endgroup$

share|cite|improve this question

asked Mar 31 at 19:19

Rithik KapoorRithik Kapoor

39510

share|cite|improve this question

asked Mar 31 at 19:19

Rithik KapoorRithik Kapoor

39510

asked Mar 31 at 19:19

Rithik KapoorRithik Kapoor

39510

asked Mar 31 at 19:19

Rithik KapoorRithik Kapoor

39510

1 Answer
1

active

oldest

votes

5

$begingroup$

The infinite tetration of $x$ sometimes symbolised by
$$x^x^x^...=e^-W(-ln(x))$$
only converges for $frac1e^ele x le e^frac1e$ when $xinmathbbR$. So the integral of this function would only be defined over this region also.

share|cite|improve this answer

answered Mar 31 at 19:25

Peter ForemanPeter Foreman

7,3661319

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Okay so I found that, $$int left( x^x^x^.^....... right) dx = sum_n=1^infty frac (-n)^n-1(n!)Gamma(n, -ln x) $$ Now to verify this, I took the plotted the derivative of the function and compared it with the graph of y=x^y and noticed that they do not match after $x=e^1/e$, could the reason you gave be the reason they don't match?
  $endgroup$
  – Rithik Kapoor
  Mar 31 at 19:35
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The function $f(x)=x^x^x^...$ is not equivalent to $y=x^y$ because the latter is multivalued. $y=x^y$ is undefined outside of the range $0lt xle e^frac1e$
  $endgroup$
  – Peter Foreman
  Mar 31 at 19:40
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry for incomplete details. Here is the graph desmos.com/calculator/kicqyk6nmw. So is the reason you gave the reason they don't match?
  $endgroup$
  – Rithik Kapoor
  Mar 31 at 19:43
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  These two graphs match in the range $frac1e^ele xle e^frac1e$ in the limit as infinite terms are taken of the expansion.
  $endgroup$
  – Peter Foreman
  Mar 31 at 19:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  So,$$int left( x^x^x^.^....... right) dx = sum_n=1^infty frac (-n)^n-1(n!)Gamma(n, -ln x) $$ in the range 1/e^e to e^(1/e) right?
  $endgroup$
  – Rithik Kapoor
  Mar 31 at 19:50
  

  
  
  
  

 | 
show 2 more comments

5

$begingroup$

The infinite tetration of $x$ sometimes symbolised by
$$x^x^x^...=e^-W(-ln(x))$$
only converges for $frac1e^ele x le e^frac1e$ when $xinmathbbR$. So the integral of this function would only be defined over this region also.

share|cite|improve this answer

answered Mar 31 at 19:25

Peter ForemanPeter Foreman

7,3661319

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Okay so I found that, $$int left( x^x^x^.^....... right) dx = sum_n=1^infty frac (-n)^n-1(n!)Gamma(n, -ln x) $$ Now to verify this, I took the plotted the derivative of the function and compared it with the graph of y=x^y and noticed that they do not match after $x=e^1/e$, could the reason you gave be the reason they don't match?
  $endgroup$
  – Rithik Kapoor
  Mar 31 at 19:35
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The function $f(x)=x^x^x^...$ is not equivalent to $y=x^y$ because the latter is multivalued. $y=x^y$ is undefined outside of the range $0lt xle e^frac1e$
  $endgroup$
  – Peter Foreman
  Mar 31 at 19:40
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry for incomplete details. Here is the graph desmos.com/calculator/kicqyk6nmw. So is the reason you gave the reason they don't match?
  $endgroup$
  – Rithik Kapoor
  Mar 31 at 19:43
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  These two graphs match in the range $frac1e^ele xle e^frac1e$ in the limit as infinite terms are taken of the expansion.
  $endgroup$
  – Peter Foreman
  Mar 31 at 19:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  So,$$int left( x^x^x^.^....... right) dx = sum_n=1^infty frac (-n)^n-1(n!)Gamma(n, -ln x) $$ in the range 1/e^e to e^(1/e) right?
  $endgroup$
  – Rithik Kapoor
  Mar 31 at 19:50
  

  
  
  
  

 | 
show 2 more comments

5

$begingroup$

The infinite tetration of $x$ sometimes symbolised by
$$x^x^x^...=e^-W(-ln(x))$$
only converges for $frac1e^ele x le e^frac1e$ when $xinmathbbR$. So the integral of this function would only be defined over this region also.

share|cite|improve this answer

answered Mar 31 at 19:25

Peter ForemanPeter Foreman

7,3661319

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Okay so I found that, $$int left( x^x^x^.^....... right) dx = sum_n=1^infty frac (-n)^n-1(n!)Gamma(n, -ln x) $$ Now to verify this, I took the plotted the derivative of the function and compared it with the graph of y=x^y and noticed that they do not match after $x=e^1/e$, could the reason you gave be the reason they don't match?
  $endgroup$
  – Rithik Kapoor
  Mar 31 at 19:35
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The function $f(x)=x^x^x^...$ is not equivalent to $y=x^y$ because the latter is multivalued. $y=x^y$ is undefined outside of the range $0lt xle e^frac1e$
  $endgroup$
  – Peter Foreman
  Mar 31 at 19:40
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry for incomplete details. Here is the graph desmos.com/calculator/kicqyk6nmw. So is the reason you gave the reason they don't match?
  $endgroup$
  – Rithik Kapoor
  Mar 31 at 19:43
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  These two graphs match in the range $frac1e^ele xle e^frac1e$ in the limit as infinite terms are taken of the expansion.
  $endgroup$
  – Peter Foreman
  Mar 31 at 19:46
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  So,$$int left( x^x^x^.^....... right) dx = sum_n=1^infty frac (-n)^n-1(n!)Gamma(n, -ln x) $$ in the range 1/e^e to e^(1/e) right?
  $endgroup$
  – Rithik Kapoor
  Mar 31 at 19:50
  

  
  
  
  

 | 
show 2 more comments

$begingroup$

The infinite tetration of $x$ sometimes symbolised by
$$x^x^x^...=e^-W(-ln(x))$$
only converges for $frac1e^ele x le e^frac1e$ when $xinmathbbR$. So the integral of this function would only be defined over this region also.

share|cite|improve this answer

answered Mar 31 at 19:25

Peter ForemanPeter Foreman

7,3661319

$endgroup$

share|cite|improve this answer

answered Mar 31 at 19:25

Peter ForemanPeter Foreman

7,3661319

answered Mar 31 at 19:25

Peter ForemanPeter Foreman

7,3661319

answered Mar 31 at 19:25

Peter ForemanPeter Foreman

7,3661319