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







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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















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







share|cite|improve this question




















  • 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













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







share|cite|improve this question















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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








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














  • 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










1 Answer
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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.






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    1 Answer
    1






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    1 Answer
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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.






    share|cite|improve this answer



























      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.






      share|cite|improve this answer

























        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.






        share|cite|improve this answer














        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.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Jun 8 at 15:57

























        answered Jun 8 at 15:50









        Mariusz Iwaniuk

        1,8571716




        1,8571716






























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