Sum Involving Gamma Function
0
$begingroup$
I see in a forum could you explain where come from
$$sum _{n=0}^{infty } frac{n! Gamma (n+1,-1) binom{k-1}{n}}{e Gamma (n+1)}=Gamma (k)$$
calculus
edited Dec 24 '18 at 20:56
Jam
4,98421431
asked Nov 18 '13 at 23:54
capeacapea
16619
$endgroup$
add a comment |
0
$begingroup$
I see in a forum could you explain where come from
$$sum _{n=0}^{infty } frac{n! Gamma (n+1,-1) binom{k-1}{n}}{e Gamma (n+1)}=Gamma (k)$$
calculus
edited Dec 24 '18 at 20:56
Jam
4,98421431
asked Nov 18 '13 at 23:54
capeacapea
16619
$endgroup$
$begingroup$
Maybe this equation would help: en.wikipedia.org/wiki/Incomplete_gamma_function#Properties
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:21
$begingroup$
Also $Gamma(n+1) = n!$ so there is some easy cancellation that takes place. Maybe there is a typo?
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:22
$begingroup$
@StephenMontgomery-Smith I also think there is a typo, because I've been trying to solve this and got nothing but disappointment :P
$endgroup$
– Ana Galois
Nov 19 '13 at 0:36
$begingroup$
Did you check the series to see if it even converges?
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:39
$begingroup$
@StephenMontgomery-Smith oh... I commit a rookie mistake and didn't checked convergence first. But it seems that it diverges to $+infty$ I'm not sure, however we still need the correction.
$endgroup$
– Ana Galois
Nov 19 '13 at 1:09
add a comment |
0
0
0
1
$begingroup$
I see in a forum could you explain where come from
$$sum _{n=0}^{infty } frac{n! Gamma (n+1,-1) binom{k-1}{n}}{e Gamma (n+1)}=Gamma (k)$$
calculus
edited Dec 24 '18 at 20:56
Jam
4,98421431
asked Nov 18 '13 at 23:54
capeacapea
16619
$endgroup$
I see in a forum could you explain where come from
$$sum _{n=0}^{infty } frac{n! Gamma (n+1,-1) binom{k-1}{n}}{e Gamma (n+1)}=Gamma (k)$$
calculus
calculus
edited Dec 24 '18 at 20:56
Jam
4,98421431
asked Nov 18 '13 at 23:54
capeacapea
16619
edited Dec 24 '18 at 20:56
Jam
4,98421431
asked Nov 18 '13 at 23:54
capeacapea
16619
edited Dec 24 '18 at 20:56
Jam
4,98421431
edited Dec 24 '18 at 20:56
Jam
4,98421431
edited Dec 24 '18 at 20:56
Jam
4,98421431
4,98421431
asked Nov 18 '13 at 23:54
capeacapea
16619
asked Nov 18 '13 at 23:54
capeacapea
16619
asked Nov 18 '13 at 23:54
capeacapea
16619
16619
$begingroup$
Maybe this equation would help: en.wikipedia.org/wiki/Incomplete_gamma_function#Properties
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:21
$begingroup$
Also $Gamma(n+1) = n!$ so there is some easy cancellation that takes place. Maybe there is a typo?
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:22
$begingroup$
@StephenMontgomery-Smith I also think there is a typo, because I've been trying to solve this and got nothing but disappointment :P
$endgroup$
– Ana Galois
Nov 19 '13 at 0:36
$begingroup$
Did you check the series to see if it even converges?
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:39
$begingroup$
@StephenMontgomery-Smith oh... I commit a rookie mistake and didn't checked convergence first. But it seems that it diverges to $+infty$ I'm not sure, however we still need the correction.
$endgroup$
– Ana Galois
Nov 19 '13 at 1:09
add a comment |
$begingroup$
Maybe this equation would help: en.wikipedia.org/wiki/Incomplete_gamma_function#Properties
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:21
$begingroup$
Also $Gamma(n+1) = n!$ so there is some easy cancellation that takes place. Maybe there is a typo?
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:22
$begingroup$
@StephenMontgomery-Smith I also think there is a typo, because I've been trying to solve this and got nothing but disappointment :P
$endgroup$
– Ana Galois
Nov 19 '13 at 0:36
$begingroup$
Did you check the series to see if it even converges?
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:39
$begingroup$
@StephenMontgomery-Smith oh... I commit a rookie mistake and didn't checked convergence first. But it seems that it diverges to $+infty$ I'm not sure, however we still need the correction.
$endgroup$
– Ana Galois
Nov 19 '13 at 1:09
$begingroup$
Maybe this equation would help: en.wikipedia.org/wiki/Incomplete_gamma_function#Properties
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:21
$begingroup$
Maybe this equation would help: en.wikipedia.org/wiki/Incomplete_gamma_function#Properties
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:21
$begingroup$
Also $Gamma(n+1) = n!$ so there is some easy cancellation that takes place. Maybe there is a typo?
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:22
$begingroup$
Also $Gamma(n+1) = n!$ so there is some easy cancellation that takes place. Maybe there is a typo?
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:22
$begingroup$
@StephenMontgomery-Smith I also think there is a typo, because I've been trying to solve this and got nothing but disappointment :P
$endgroup$
– Ana Galois
Nov 19 '13 at 0:36
$begingroup$
@StephenMontgomery-Smith I also think there is a typo, because I've been trying to solve this and got nothing but disappointment :P
$endgroup$
– Ana Galois
Nov 19 '13 at 0:36
$begingroup$
Did you check the series to see if it even converges?
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:39
$begingroup$
Did you check the series to see if it even converges?
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:39
$begingroup$
@StephenMontgomery-Smith oh... I commit a rookie mistake and didn't checked convergence first. But it seems that it diverges to $+infty$ I'm not sure, however we still need the correction.
$endgroup$
– Ana Galois
Nov 19 '13 at 1:09
$begingroup$
@StephenMontgomery-Smith oh... I commit a rookie mistake and didn't checked convergence first. But it seems that it diverges to $+infty$ I'm not sure, however we still need the correction.
$endgroup$
– Ana Galois
Nov 19 '13 at 1:09
add a comment |
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$begingroup$
Maybe this equation would help: en.wikipedia.org/wiki/Incomplete_gamma_function#Properties
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:21
$begingroup$
Also $Gamma(n+1) = n!$ so there is some easy cancellation that takes place. Maybe there is a typo?
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:22
$begingroup$
@StephenMontgomery-Smith I also think there is a typo, because I've been trying to solve this and got nothing but disappointment :P
$endgroup$
– Ana Galois
Nov 19 '13 at 0:36
$begingroup$
Did you check the series to see if it even converges?
$endgroup$
– Stephen Montgomery-Smith
Nov 19 '13 at 0:39
$begingroup$
@StephenMontgomery-Smith oh... I commit a rookie mistake and didn't checked convergence first. But it seems that it diverges to $+infty$ I'm not sure, however we still need the correction.
$endgroup$
– Ana Galois
Nov 19 '13 at 1:09