On the regularized gamma function (analysis problem)
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I have a quick question on the regularized gamma function, defined as
$Q (a,z)=frac{Gamma(a,z)}{Gamma(a)} ,. [1]$
What is the value of $Q (a,z)$ in the asymptotic limits $a rightarrow infty$ and $z rightarrow infty$ ?
[1] see http://mathworld.wolfram.com/RegularizedGammaFunction.html
real-analysis gamma-function
asked Nov 18 at 1:10
Nath
437
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up vote
1
down vote
favorite
I have a quick question on the regularized gamma function, defined as
$Q (a,z)=frac{Gamma(a,z)}{Gamma(a)} ,. [1]$
What is the value of $Q (a,z)$ in the asymptotic limits $a rightarrow infty$ and $z rightarrow infty$ ?
[1] see http://mathworld.wolfram.com/RegularizedGammaFunction.html
real-analysis gamma-function
asked Nov 18 at 1:10
Nath
437
The limit and asymptotic as $a to +infty $ is not hard, what did you try ?
– reuns
Nov 18 at 4:28
I am not familiar with asymptotic calculus. But what I tried as a first guest is to increase $(a,z)$ using Mathematica and the regularized gamma function is shown to increase. So I guess that, as $(a,z) rightarrow infty$, since the function is bound between 0 and 1, that it saturates to 1. What do you think about that ?
– Nath
Nov 18 at 12:19
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I have a quick question on the regularized gamma function, defined as
$Q (a,z)=frac{Gamma(a,z)}{Gamma(a)} ,. [1]$
What is the value of $Q (a,z)$ in the asymptotic limits $a rightarrow infty$ and $z rightarrow infty$ ?
[1] see http://mathworld.wolfram.com/RegularizedGammaFunction.html
real-analysis gamma-function
asked Nov 18 at 1:10
Nath
437
I have a quick question on the regularized gamma function, defined as
$Q (a,z)=frac{Gamma(a,z)}{Gamma(a)} ,. [1]$
What is the value of $Q (a,z)$ in the asymptotic limits $a rightarrow infty$ and $z rightarrow infty$ ?
[1] see http://mathworld.wolfram.com/RegularizedGammaFunction.html
real-analysis gamma-function
real-analysis gamma-function
asked Nov 18 at 1:10
Nath
437
asked Nov 18 at 1:10
Nath
437
asked Nov 18 at 1:10
Nath
437
asked Nov 18 at 1:10
Nath
437
asked Nov 18 at 1:10
Nath
437
437
The limit and asymptotic as $a to +infty $ is not hard, what did you try ?
– reuns
Nov 18 at 4:28
I am not familiar with asymptotic calculus. But what I tried as a first guest is to increase $(a,z)$ using Mathematica and the regularized gamma function is shown to increase. So I guess that, as $(a,z) rightarrow infty$, since the function is bound between 0 and 1, that it saturates to 1. What do you think about that ?
– Nath
Nov 18 at 12:19
add a comment |
The limit and asymptotic as $a to +infty $ is not hard, what did you try ?
– reuns
Nov 18 at 4:28
I am not familiar with asymptotic calculus. But what I tried as a first guest is to increase $(a,z)$ using Mathematica and the regularized gamma function is shown to increase. So I guess that, as $(a,z) rightarrow infty$, since the function is bound between 0 and 1, that it saturates to 1. What do you think about that ?
– Nath
Nov 18 at 12:19
The limit and asymptotic as $a to +infty $ is not hard, what did you try ?
– reuns
Nov 18 at 4:28
The limit and asymptotic as $a to +infty $ is not hard, what did you try ?
– reuns
Nov 18 at 4:28
I am not familiar with asymptotic calculus. But what I tried as a first guest is to increase $(a,z)$ using Mathematica and the regularized gamma function is shown to increase. So I guess that, as $(a,z) rightarrow infty$, since the function is bound between 0 and 1, that it saturates to 1. What do you think about that ?
– Nath
Nov 18 at 12:19
I am not familiar with asymptotic calculus. But what I tried as a first guest is to increase $(a,z)$ using Mathematica and the regularized gamma function is shown to increase. So I guess that, as $(a,z) rightarrow infty$, since the function is bound between 0 and 1, that it saturates to 1. What do you think about that ?
– Nath
Nov 18 at 12:19
add a comment |
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The limit and asymptotic as $a to +infty $ is not hard, what did you try ?
– reuns
Nov 18 at 4:28
I am not familiar with asymptotic calculus. But what I tried as a first guest is to increase $(a,z)$ using Mathematica and the regularized gamma function is shown to increase. So I guess that, as $(a,z) rightarrow infty$, since the function is bound between 0 and 1, that it saturates to 1. What do you think about that ?
– Nath
Nov 18 at 12:19