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8-Gravel
February 6, 2024
Solved

Gamma function

  • February 6, 2024
  • 2 replies
  • 1538 views

hello everyone!

I want to set this equation equal to zero and find the unknowns c and k. Of course, I have to use the gamma function for this. Does anyone know this subject?

Best answer by Werner_E

Solving just ONE equation for TWO different variables??

 

You can solve the equation symbolically for one of the variables and get the solution dependent on the other

Werner_E_0-1707265514880.png

You may add "simplify"

Werner_E_3-1707265780208.png

 

Solving for k fails, though,

Werner_E_2-1707265586416.png

and the reason my be that there is no unique inverse of the Gamma function.

But given a numeric value for c you can solve for k

Werner_E_4-1707265997236.png

You my also use a solve block with find or the numeric "root" function to get the solution

Here I am looking for a solution in the range from 0.1 to 4

Werner_E_7-1707266403729.png

But there is a second solution and I let "root" look for it in the range from 4 to 10

Werner_E_8-1707266419376.png

Here the plot so its clear why we have two solutions if c=4.565:

Werner_E_9-1707266452831.png

 

 

 

2 replies

ttokoro
21-Topaz I
21-Topaz I
February 7, 2024

One of the answers.

image.png

t.t.
Werner_E25-Diamond IAnswer
25-Diamond I
February 7, 2024

Solving just ONE equation for TWO different variables??

 

You can solve the equation symbolically for one of the variables and get the solution dependent on the other

Werner_E_0-1707265514880.png

You may add "simplify"

Werner_E_3-1707265780208.png

 

Solving for k fails, though,

Werner_E_2-1707265586416.png

and the reason my be that there is no unique inverse of the Gamma function.

But given a numeric value for c you can solve for k

Werner_E_4-1707265997236.png

You my also use a solve block with find or the numeric "root" function to get the solution

Here I am looking for a solution in the range from 0.1 to 4

Werner_E_7-1707266403729.png

But there is a second solution and I let "root" look for it in the range from 4 to 10

Werner_E_8-1707266419376.png

Here the plot so its clear why we have two solutions if c=4.565:

Werner_E_9-1707266452831.png

 

 

 

8-Gravel
February 7, 2024

thank you!