limit of variant form of incomplete Gamma function

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What is the limit of



$$lim_MrightarrowinftyMfrac(Mt)^Me^-MtM!$$



where $0<t<infty$, $MinmathbbN$



It is supposed to be 0 by the data observed but i could not prove it theoretically.




limits




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    up vote
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    down vote

    favorite












    What is the limit of



    $$lim_MrightarrowinftyMfrac(Mt)^Me^-MtM!$$



    where $0<t<infty$, $MinmathbbN$



    It is supposed to be 0 by the data observed but i could not prove it theoretically.




    limits




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      What is the limit of



      $$lim_MrightarrowinftyMfrac(Mt)^Me^-MtM!$$



      where $0<t<infty$, $MinmathbbN$



      It is supposed to be 0 by the data observed but i could not prove it theoretically.




      limits




      share|cite|improve this question











      What is the limit of



      $$lim_MrightarrowinftyMfrac(Mt)^Me^-MtM!$$



      where $0<t<infty$, $MinmathbbN$



      It is supposed to be 0 by the data observed but i could not prove it theoretically.





      limits





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Aug 2 at 18:10









      Sherry

      63




      63




















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          Using Stirling's formula for $M!$ we get
          $$
          M,frac(M,t)^Me^-MtM!simsqrtfracM2,pi,t^M,e^-Mt.
          $$






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            1 Answer
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            up vote
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            accepted










            Using Stirling's formula for $M!$ we get
            $$
            M,frac(M,t)^Me^-MtM!simsqrtfracM2,pi,t^M,e^-Mt.
            $$






            share|cite|improve this answer

























              up vote
              0
              down vote



              accepted










              Using Stirling's formula for $M!$ we get
              $$
              M,frac(M,t)^Me^-MtM!simsqrtfracM2,pi,t^M,e^-Mt.
              $$






              share|cite|improve this answer























                up vote
                0
                down vote



                accepted







                up vote
                0
                down vote



                accepted






                Using Stirling's formula for $M!$ we get
                $$
                M,frac(M,t)^Me^-MtM!simsqrtfracM2,pi,t^M,e^-Mt.
                $$






                share|cite|improve this answer













                Using Stirling's formula for $M!$ we get
                $$
                M,frac(M,t)^Me^-MtM!simsqrtfracM2,pi,t^M,e^-Mt.
                $$







                share|cite|improve this answer













                share|cite|improve this answer



                share|cite|improve this answer











                answered Aug 2 at 18:22









                Julián Aguirre

                64.4k23894




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