Integral $int e^{-theta^{beta}}(theta^{beta})^{n}dbeta$
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For parameter $theta$, i was integrating $int e^{-theta^{beta}}(theta^{beta})^{n}dbeta$, because i can't solve it using substitusion or partial integral, so i used wolframalpha to calculate it, but the outcome is, (no result found in terms of standard mathematical function). What 'not standard' mathematical function that could solve the integral? And if i give lower and upper bound, is it now be able to calculated? may be by numerically or something?
calculus integration
edited Jun 8 at 15:39
Arjang
5,56662363
add a comment |
up vote
-2
down vote
favorite
For parameter $theta$, i was integrating $int e^{-theta^{beta}}(theta^{beta})^{n}dbeta$, because i can't solve it using substitusion or partial integral, so i used wolframalpha to calculate it, but the outcome is, (no result found in terms of standard mathematical function). What 'not standard' mathematical function that could solve the integral? And if i give lower and upper bound, is it now be able to calculated? may be by numerically or something?
calculus integration
edited Jun 8 at 15:39
Arjang
5,56662363
1
i downt know why it is being clicked down, just give me the reason why instead of click down! thx
– user501869
Jun 8 at 15:18
After a change of variable, it should be an incomplete gamma function.
– Cameron Williams
Jun 8 at 15:44
@Ab Rohi, I didnt downvote this, but reading it made me feel angry, because 1.It looks like you just put jibberish together, what is this or what is the motivation , where is your work to show you tried something, have you spend 10 minutes looking at the other integration questions here? the question makes the reader think that you dont know anything and are wasting their time, it looks like complete nonsense, I tried to fix it, please take time to explain what,why,how
– Arjang
Jun 8 at 15:44
1
@Arjang thanks you for not being downvote this, so i m doing some project and in the middle of project, there is that function that ,must be integrated, that's why im panicking, because there is the deadline and i haven't found how to solve it.
– user501869
Jun 8 at 15:48
1
@CameronWilliams i just read on wikipedia for incomplete gamma function, thank you for your good reference!
– user501869
Jun 8 at 15:49
add a comment |
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
For parameter $theta$, i was integrating $int e^{-theta^{beta}}(theta^{beta})^{n}dbeta$, because i can't solve it using substitusion or partial integral, so i used wolframalpha to calculate it, but the outcome is, (no result found in terms of standard mathematical function). What 'not standard' mathematical function that could solve the integral? And if i give lower and upper bound, is it now be able to calculated? may be by numerically or something?
calculus integration
edited Jun 8 at 15:39
Arjang
5,56662363
For parameter $theta$, i was integrating $int e^{-theta^{beta}}(theta^{beta})^{n}dbeta$, because i can't solve it using substitusion or partial integral, so i used wolframalpha to calculate it, but the outcome is, (no result found in terms of standard mathematical function). What 'not standard' mathematical function that could solve the integral? And if i give lower and upper bound, is it now be able to calculated? may be by numerically or something?
calculus integration
calculus integration
edited Jun 8 at 15:39
Arjang
5,56662363
edited Jun 8 at 15:39
Arjang
5,56662363
edited Jun 8 at 15:39
Arjang
5,56662363
edited Jun 8 at 15:39
Arjang
5,56662363
edited Jun 8 at 15:39
Arjang
5,56662363
5,56662363
asked Jun 8 at 15:15
user501869
1
i downt know why it is being clicked down, just give me the reason why instead of click down! thx
– user501869
Jun 8 at 15:18
After a change of variable, it should be an incomplete gamma function.
– Cameron Williams
Jun 8 at 15:44
@Ab Rohi, I didnt downvote this, but reading it made me feel angry, because 1.It looks like you just put jibberish together, what is this or what is the motivation , where is your work to show you tried something, have you spend 10 minutes looking at the other integration questions here? the question makes the reader think that you dont know anything and are wasting their time, it looks like complete nonsense, I tried to fix it, please take time to explain what,why,how
– Arjang
Jun 8 at 15:44
1
@Arjang thanks you for not being downvote this, so i m doing some project and in the middle of project, there is that function that ,must be integrated, that's why im panicking, because there is the deadline and i haven't found how to solve it.
– user501869
Jun 8 at 15:48
1
@CameronWilliams i just read on wikipedia for incomplete gamma function, thank you for your good reference!
– user501869
Jun 8 at 15:49
add a comment |
1
i downt know why it is being clicked down, just give me the reason why instead of click down! thx
– user501869
Jun 8 at 15:18
After a change of variable, it should be an incomplete gamma function.
– Cameron Williams
Jun 8 at 15:44
@Ab Rohi, I didnt downvote this, but reading it made me feel angry, because 1.It looks like you just put jibberish together, what is this or what is the motivation , where is your work to show you tried something, have you spend 10 minutes looking at the other integration questions here? the question makes the reader think that you dont know anything and are wasting their time, it looks like complete nonsense, I tried to fix it, please take time to explain what,why,how
– Arjang
Jun 8 at 15:44
1
@Arjang thanks you for not being downvote this, so i m doing some project and in the middle of project, there is that function that ,must be integrated, that's why im panicking, because there is the deadline and i haven't found how to solve it.
– user501869
Jun 8 at 15:48
1
@CameronWilliams i just read on wikipedia for incomplete gamma function, thank you for your good reference!
– user501869
Jun 8 at 15:49
1
1
i downt know why it is being clicked down, just give me the reason why instead of click down! thx
– user501869
Jun 8 at 15:18
i downt know why it is being clicked down, just give me the reason why instead of click down! thx
– user501869
Jun 8 at 15:18
After a change of variable, it should be an incomplete gamma function.
– Cameron Williams
Jun 8 at 15:44
After a change of variable, it should be an incomplete gamma function.
– Cameron Williams
Jun 8 at 15:44
@Ab Rohi, I didnt downvote this, but reading it made me feel angry, because 1.It looks like you just put jibberish together, what is this or what is the motivation , where is your work to show you tried something, have you spend 10 minutes looking at the other integration questions here? the question makes the reader think that you dont know anything and are wasting their time, it looks like complete nonsense, I tried to fix it, please take time to explain what,why,how
– Arjang
Jun 8 at 15:44
@Ab Rohi, I didnt downvote this, but reading it made me feel angry, because 1.It looks like you just put jibberish together, what is this or what is the motivation , where is your work to show you tried something, have you spend 10 minutes looking at the other integration questions here? the question makes the reader think that you dont know anything and are wasting their time, it looks like complete nonsense, I tried to fix it, please take time to explain what,why,how
– Arjang
Jun 8 at 15:44
1
1
@Arjang thanks you for not being downvote this, so i m doing some project and in the middle of project, there is that function that ,must be integrated, that's why im panicking, because there is the deadline and i haven't found how to solve it.
– user501869
Jun 8 at 15:48
@Arjang thanks you for not being downvote this, so i m doing some project and in the middle of project, there is that function that ,must be integrated, that's why im panicking, because there is the deadline and i haven't found how to solve it.
– user501869
Jun 8 at 15:48
1
1
@CameronWilliams i just read on wikipedia for incomplete gamma function, thank you for your good reference!
– user501869
Jun 8 at 15:49
@CameronWilliams i just read on wikipedia for incomplete gamma function, thank you for your good reference!
– user501869
Jun 8 at 15:49
add a comment |
1 Answer
1
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oldest
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up vote
2
down vote
With CAS Help and Mellin Transform:
$$color{blue}{int e^{-theta ^{beta }} theta ^{n beta } , dbeta} =\int mathcal{M}_Aleft[e^{-A* theta ^{beta }} theta ^{n beta }right](s) ,
dbeta =\int theta ^{n beta } left(theta ^{beta }right)^{-s} Gamma (s) , dbeta =\mathcal{M}_s^{-1}left[frac{theta ^{n beta
} left(theta ^{beta }right)^{-s} Gamma (s)}{n log (theta )-s log (theta )}right](1)=\-frac{pi csc (n pi ) left(Gamma
(1+n)-n Gamma left(n,0,theta ^{beta }right)right)}{Gamma (1-n) Gamma (1+n) log (theta )}+C=color{blue}{\-frac{Gamma left(n,theta ^{beta }right)}{log (theta )}+C}$$
where: $Gamma left(n,theta ^{beta }right)$ is incomplete gamma function.
answered Jun 8 at 15:50
Mariusz Iwaniuk
1,8571716
add a comment |
Your Answer
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1 Answer
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1 Answer
1
active
oldest
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oldest
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active
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up vote
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With CAS Help and Mellin Transform:
$$color{blue}{int e^{-theta ^{beta }} theta ^{n beta } , dbeta} =\int mathcal{M}_Aleft[e^{-A* theta ^{beta }} theta ^{n beta }right](s) ,
dbeta =\int theta ^{n beta } left(theta ^{beta }right)^{-s} Gamma (s) , dbeta =\mathcal{M}_s^{-1}left[frac{theta ^{n beta
} left(theta ^{beta }right)^{-s} Gamma (s)}{n log (theta )-s log (theta )}right](1)=\-frac{pi csc (n pi ) left(Gamma
(1+n)-n Gamma left(n,0,theta ^{beta }right)right)}{Gamma (1-n) Gamma (1+n) log (theta )}+C=color{blue}{\-frac{Gamma left(n,theta ^{beta }right)}{log (theta )}+C}$$
where: $Gamma left(n,theta ^{beta }right)$ is incomplete gamma function.
answered Jun 8 at 15:50
Mariusz Iwaniuk
1,8571716
add a comment |
up vote
2
down vote
With CAS Help and Mellin Transform:
$$color{blue}{int e^{-theta ^{beta }} theta ^{n beta } , dbeta} =\int mathcal{M}_Aleft[e^{-A* theta ^{beta }} theta ^{n beta }right](s) ,
dbeta =\int theta ^{n beta } left(theta ^{beta }right)^{-s} Gamma (s) , dbeta =\mathcal{M}_s^{-1}left[frac{theta ^{n beta
} left(theta ^{beta }right)^{-s} Gamma (s)}{n log (theta )-s log (theta )}right](1)=\-frac{pi csc (n pi ) left(Gamma
(1+n)-n Gamma left(n,0,theta ^{beta }right)right)}{Gamma (1-n) Gamma (1+n) log (theta )}+C=color{blue}{\-frac{Gamma left(n,theta ^{beta }right)}{log (theta )}+C}$$
where: $Gamma left(n,theta ^{beta }right)$ is incomplete gamma function.
answered Jun 8 at 15:50
Mariusz Iwaniuk
1,8571716
add a comment |
up vote
2
down vote
up vote
2
down vote
With CAS Help and Mellin Transform:
$$color{blue}{int e^{-theta ^{beta }} theta ^{n beta } , dbeta} =\int mathcal{M}_Aleft[e^{-A* theta ^{beta }} theta ^{n beta }right](s) ,
dbeta =\int theta ^{n beta } left(theta ^{beta }right)^{-s} Gamma (s) , dbeta =\mathcal{M}_s^{-1}left[frac{theta ^{n beta
} left(theta ^{beta }right)^{-s} Gamma (s)}{n log (theta )-s log (theta )}right](1)=\-frac{pi csc (n pi ) left(Gamma
(1+n)-n Gamma left(n,0,theta ^{beta }right)right)}{Gamma (1-n) Gamma (1+n) log (theta )}+C=color{blue}{\-frac{Gamma left(n,theta ^{beta }right)}{log (theta )}+C}$$
where: $Gamma left(n,theta ^{beta }right)$ is incomplete gamma function.
answered Jun 8 at 15:50
Mariusz Iwaniuk
1,8571716
With CAS Help and Mellin Transform:
$$color{blue}{int e^{-theta ^{beta }} theta ^{n beta } , dbeta} =\int mathcal{M}_Aleft[e^{-A* theta ^{beta }} theta ^{n beta }right](s) ,
dbeta =\int theta ^{n beta } left(theta ^{beta }right)^{-s} Gamma (s) , dbeta =\mathcal{M}_s^{-1}left[frac{theta ^{n beta
} left(theta ^{beta }right)^{-s} Gamma (s)}{n log (theta )-s log (theta )}right](1)=\-frac{pi csc (n pi ) left(Gamma
(1+n)-n Gamma left(n,0,theta ^{beta }right)right)}{Gamma (1-n) Gamma (1+n) log (theta )}+C=color{blue}{\-frac{Gamma left(n,theta ^{beta }right)}{log (theta )}+C}$$
where: $Gamma left(n,theta ^{beta }right)$ is incomplete gamma function.
answered Jun 8 at 15:50
Mariusz Iwaniuk
1,8571716
edited Jun 8 at 15:57
answered Jun 8 at 15:50
Mariusz Iwaniuk
1,8571716
answered Jun 8 at 15:50
Mariusz Iwaniuk
1,8571716
answered Jun 8 at 15:50
Mariusz Iwaniuk
1,8571716
1,8571716
add a comment |
add a comment |
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1
i downt know why it is being clicked down, just give me the reason why instead of click down! thx
– user501869
Jun 8 at 15:18
After a change of variable, it should be an incomplete gamma function.
– Cameron Williams
Jun 8 at 15:44
@Ab Rohi, I didnt downvote this, but reading it made me feel angry, because 1.It looks like you just put jibberish together, what is this or what is the motivation , where is your work to show you tried something, have you spend 10 minutes looking at the other integration questions here? the question makes the reader think that you dont know anything and are wasting their time, it looks like complete nonsense, I tried to fix it, please take time to explain what,why,how
– Arjang
Jun 8 at 15:44
1
@Arjang thanks you for not being downvote this, so i m doing some project and in the middle of project, there is that function that ,must be integrated, that's why im panicking, because there is the deadline and i haven't found how to solve it.
– user501869
Jun 8 at 15:48
1
@CameronWilliams i just read on wikipedia for incomplete gamma function, thank you for your good reference!
– user501869
Jun 8 at 15:49