Numerical evaluation of $sum_{N=1}^inftyleft(frac{1}{Gamma(N+1)^2}right)^{frac{1}{N}}$
0
Given
$$S=sum_{N=1}^inftyleft(dfrac{1}{Gamma(N+1)^2}right)^{dfrac{1}{N}}$$
Using the Carleman inequality, I got for S:
$$Sledfrac{1}{6}epi^2$$
Using numerical calculation I suppose that the value of
S is less than $3.2$.
Is it possible to have a better vaule or eventually a better iniquality for S?
sequences-and-series inequality gamma-function
edited Nov 27 at 11:44
GNUSupporter 8964民主女神 地下教會
12.8k72445
asked Nov 27 at 11:28
Riccardo.Alestra
5,93412153
add a comment |
0
Given
$$S=sum_{N=1}^inftyleft(dfrac{1}{Gamma(N+1)^2}right)^{dfrac{1}{N}}$$
Using the Carleman inequality, I got for S:
$$Sledfrac{1}{6}epi^2$$
Using numerical calculation I suppose that the value of
S is less than $3.2$.
Is it possible to have a better vaule or eventually a better iniquality for S?
sequences-and-series inequality gamma-function
edited Nov 27 at 11:44
GNUSupporter 8964民主女神 地下教會
12.8k72445
asked Nov 27 at 11:28
Riccardo.Alestra
5,93412153
$3.096724440$ is better
– Claude Leibovici
Nov 27 at 11:44
I have changed the formatting of the title so as to make it take up less vertical space -- this is a policy to ensure that the scarce space on the main page is distributed evenly over the questions. See here for more information. Please take this into consideration for future questions. Thanks in advance.
– GNUSupporter 8964民主女神 地下教會
Nov 27 at 11:45
PARI/GP easily eats $texttt{sumnum(n=1,exp(-2*lngamma(n+1)/n))}$ giving $3.09672480007969548412482407485480297466758470220341ldots$
– metamorphy
Nov 27 at 12:32
add a comment |
0
0
0
1
Given
$$S=sum_{N=1}^inftyleft(dfrac{1}{Gamma(N+1)^2}right)^{dfrac{1}{N}}$$
Using the Carleman inequality, I got for S:
$$Sledfrac{1}{6}epi^2$$
Using numerical calculation I suppose that the value of
S is less than $3.2$.
Is it possible to have a better vaule or eventually a better iniquality for S?
sequences-and-series inequality gamma-function
edited Nov 27 at 11:44
GNUSupporter 8964民主女神 地下教會
12.8k72445
asked Nov 27 at 11:28
Riccardo.Alestra
5,93412153
Given
$$S=sum_{N=1}^inftyleft(dfrac{1}{Gamma(N+1)^2}right)^{dfrac{1}{N}}$$
Using the Carleman inequality, I got for S:
$$Sledfrac{1}{6}epi^2$$
Using numerical calculation I suppose that the value of
S is less than $3.2$.
Is it possible to have a better vaule or eventually a better iniquality for S?
sequences-and-series inequality gamma-function
sequences-and-series inequality gamma-function
edited Nov 27 at 11:44
GNUSupporter 8964民主女神 地下教會
12.8k72445
asked Nov 27 at 11:28
Riccardo.Alestra
5,93412153
edited Nov 27 at 11:44
GNUSupporter 8964民主女神 地下教會
12.8k72445
asked Nov 27 at 11:28
Riccardo.Alestra
5,93412153
edited Nov 27 at 11:44
GNUSupporter 8964民主女神 地下教會
12.8k72445
edited Nov 27 at 11:44
GNUSupporter 8964民主女神 地下教會
12.8k72445
edited Nov 27 at 11:44
GNUSupporter 8964民主女神 地下教會
12.8k72445
12.8k72445
asked Nov 27 at 11:28
Riccardo.Alestra
5,93412153
asked Nov 27 at 11:28
Riccardo.Alestra
5,93412153
asked Nov 27 at 11:28
Riccardo.Alestra
5,93412153
5,93412153
$3.096724440$ is better
– Claude Leibovici
Nov 27 at 11:44
I have changed the formatting of the title so as to make it take up less vertical space -- this is a policy to ensure that the scarce space on the main page is distributed evenly over the questions. See here for more information. Please take this into consideration for future questions. Thanks in advance.
– GNUSupporter 8964民主女神 地下教會
Nov 27 at 11:45
PARI/GP easily eats $texttt{sumnum(n=1,exp(-2*lngamma(n+1)/n))}$ giving $3.09672480007969548412482407485480297466758470220341ldots$
– metamorphy
Nov 27 at 12:32
add a comment |
$3.096724440$ is better
– Claude Leibovici
Nov 27 at 11:44
I have changed the formatting of the title so as to make it take up less vertical space -- this is a policy to ensure that the scarce space on the main page is distributed evenly over the questions. See here for more information. Please take this into consideration for future questions. Thanks in advance.
– GNUSupporter 8964民主女神 地下教會
Nov 27 at 11:45
PARI/GP easily eats $texttt{sumnum(n=1,exp(-2*lngamma(n+1)/n))}$ giving $3.09672480007969548412482407485480297466758470220341ldots$
– metamorphy
Nov 27 at 12:32
$3.096724440$ is better
– Claude Leibovici
Nov 27 at 11:44
$3.096724440$ is better
– Claude Leibovici
Nov 27 at 11:44
I have changed the formatting of the title so as to make it take up less vertical space -- this is a policy to ensure that the scarce space on the main page is distributed evenly over the questions. See here for more information. Please take this into consideration for future questions. Thanks in advance.
– GNUSupporter 8964民主女神 地下教會
Nov 27 at 11:45
I have changed the formatting of the title so as to make it take up less vertical space -- this is a policy to ensure that the scarce space on the main page is distributed evenly over the questions. See here for more information. Please take this into consideration for future questions. Thanks in advance.
– GNUSupporter 8964民主女神 地下教會
Nov 27 at 11:45
PARI/GP easily eats $texttt{sumnum(n=1,exp(-2*lngamma(n+1)/n))}$ giving $3.09672480007969548412482407485480297466758470220341ldots$
– metamorphy
Nov 27 at 12:32
PARI/GP easily eats $texttt{sumnum(n=1,exp(-2*lngamma(n+1)/n))}$ giving $3.09672480007969548412482407485480297466758470220341ldots$
– metamorphy
Nov 27 at 12:32
add a comment |
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$3.096724440$ is better
– Claude Leibovici
Nov 27 at 11:44
I have changed the formatting of the title so as to make it take up less vertical space -- this is a policy to ensure that the scarce space on the main page is distributed evenly over the questions. See here for more information. Please take this into consideration for future questions. Thanks in advance.
– GNUSupporter 8964民主女神 地下教會
Nov 27 at 11:45
PARI/GP easily eats $texttt{sumnum(n=1,exp(-2*lngamma(n+1)/n))}$ giving $3.09672480007969548412482407485480297466758470220341ldots$
– metamorphy
Nov 27 at 12:32