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8-Gravel
Feb 6, 2024 12:47 PM UTC
Solved

Gamma function

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?

Werner_E
Werner_EAnswer
25-Diamond I
Feb 7, 2024 12:41 AM UTC

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

 

 

 

3 replies

ttokoro
21-Topaz I
Feb 7, 2024 12:22 AM UTC

One of the answers.

image.png

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t.t.
Werner_E
Werner_E25-Diamond IAnswer
25-Diamond I
Feb 7, 2024 12:41 AM UTC

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

 

 

 

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8-Gravel
Feb 7, 2024 6:01 AM UTC

thank you!

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