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Rewrite product of exponential and incomplete gamma function in terms of Meijer's G function

0

$begingroup$

As title said, is there a way to rewrite
$$ f(x) = e^-mu_1 x Gamma(alpha, mu_2 x)$$
into MeijerG's function having the form
$
beginaligned
G^m,n_p,q
left(
beginmatrix
a_1,dots,a_n,a_n+1,dots,a_p \
b_1,dots,b_m,b_m+1,dots,b_q
endmatrix
Bigg|mu x
right)
endaligned
$ Link, where all given parameters are positive real numbers, and $alpha ge 1$.

• 
  $Gamma(alpha,x) = int_xt^alpha-1 e^-t dt$ is the incomplete gamma function Link.

exponential-function special-functions

share|cite|improve this question

asked Mar 26 at 8:50

KyleKyle

214

$endgroup$

add a comment | 

0

$begingroup$

As title said, is there a way to rewrite
$$ f(x) = e^-mu_1 x Gamma(alpha, mu_2 x)$$
into MeijerG's function having the form
$
beginaligned
G^m,n_p,q
left(
beginmatrix
a_1,dots,a_n,a_n+1,dots,a_p \
b_1,dots,b_m,b_m+1,dots,b_q
endmatrix
Bigg|mu x
right)
endaligned
$ Link, where all given parameters are positive real numbers, and $alpha ge 1$.

• 
  $Gamma(alpha,x) = int_xt^alpha-1 e^-t dt$ is the incomplete gamma function Link.

exponential-function special-functions

share|cite|improve this question

asked Mar 26 at 8:50

KyleKyle

214

$endgroup$

add a comment | 

$begingroup$

As title said, is there a way to rewrite
$$ f(x) = e^-mu_1 x Gamma(alpha, mu_2 x)$$
into MeijerG's function having the form
$
beginaligned
G^m,n_p,q
left(
beginmatrix
a_1,dots,a_n,a_n+1,dots,a_p \
b_1,dots,b_m,b_m+1,dots,b_q
endmatrix
Bigg|mu x
right)
endaligned
$ Link, where all given parameters are positive real numbers, and $alpha ge 1$.

• 
  $Gamma(alpha,x) = int_xt^alpha-1 e^-t dt$ is the incomplete gamma function Link.

exponential-function special-functions

share|cite|improve this question

asked Mar 26 at 8:50

KyleKyle

214

$endgroup$

share|cite|improve this question

asked Mar 26 at 8:50

KyleKyle

214

share|cite|improve this question

asked Mar 26 at 8:50

KyleKyle

214

asked Mar 26 at 8:50

KyleKyle

214

asked Mar 26 at 8:50

KyleKyle

214