Evaluate $sum_{k=1}^infty e^{-sqrt{2 pi k}}$
1
$begingroup$
Is there a closed form of this series
$$sum_{k=1}^infty e^{-sqrt{2 pi k}} $$
It can help to solve a very hard integral problem
$int_0^infty e^{-x}x sin(x)coth(x^2) .dx$
calculus sequences-and-series
asked Dec 18 '18 at 20:57
Ahmad AlbawAhmad Albaw
103
$endgroup$
add a comment |
1
$begingroup$
Is there a closed form of this series
$$sum_{k=1}^infty e^{-sqrt{2 pi k}} $$
It can help to solve a very hard integral problem
$int_0^infty e^{-x}x sin(x)coth(x^2) .dx$
calculus sequences-and-series
asked Dec 18 '18 at 20:57
Ahmad AlbawAhmad Albaw
103
$endgroup$
2
$begingroup$
What is that hard integral? Don't keep it for yourself please :D
$endgroup$
– Zacky
Dec 18 '18 at 21:00
$begingroup$
No closed form as per Wolfram Alpha. How did that sum arise ? What's the integral ?
$endgroup$
– Rebellos
Dec 18 '18 at 21:04
$begingroup$
Check it now it's edited
$endgroup$
– Ahmad Albaw
Dec 18 '18 at 21:11
$begingroup$
Sorry. Unsolvable........
$endgroup$
– Mostafa Ayaz
Jan 5 at 7:20
add a comment |
1
1
1
1
$begingroup$
Is there a closed form of this series
$$sum_{k=1}^infty e^{-sqrt{2 pi k}} $$
It can help to solve a very hard integral problem
$int_0^infty e^{-x}x sin(x)coth(x^2) .dx$
calculus sequences-and-series
asked Dec 18 '18 at 20:57
Ahmad AlbawAhmad Albaw
103
$endgroup$
Is there a closed form of this series
$$sum_{k=1}^infty e^{-sqrt{2 pi k}} $$
It can help to solve a very hard integral problem
$int_0^infty e^{-x}x sin(x)coth(x^2) .dx$
calculus sequences-and-series
calculus sequences-and-series
asked Dec 18 '18 at 20:57
Ahmad AlbawAhmad Albaw
103
asked Dec 18 '18 at 20:57
Ahmad AlbawAhmad Albaw
103
edited Dec 18 '18 at 21:10
Ahmad Albaw
asked Dec 18 '18 at 20:57
Ahmad AlbawAhmad Albaw
103
asked Dec 18 '18 at 20:57
Ahmad AlbawAhmad Albaw
103
asked Dec 18 '18 at 20:57
Ahmad AlbawAhmad Albaw
103
103
2
$begingroup$
What is that hard integral? Don't keep it for yourself please :D
$endgroup$
– Zacky
Dec 18 '18 at 21:00
$begingroup$
No closed form as per Wolfram Alpha. How did that sum arise ? What's the integral ?
$endgroup$
– Rebellos
Dec 18 '18 at 21:04
$begingroup$
Check it now it's edited
$endgroup$
– Ahmad Albaw
Dec 18 '18 at 21:11
$begingroup$
Sorry. Unsolvable........
$endgroup$
– Mostafa Ayaz
Jan 5 at 7:20
add a comment |
2
$begingroup$
What is that hard integral? Don't keep it for yourself please :D
$endgroup$
– Zacky
Dec 18 '18 at 21:00
$begingroup$
No closed form as per Wolfram Alpha. How did that sum arise ? What's the integral ?
$endgroup$
– Rebellos
Dec 18 '18 at 21:04
$begingroup$
Check it now it's edited
$endgroup$
– Ahmad Albaw
Dec 18 '18 at 21:11
$begingroup$
Sorry. Unsolvable........
$endgroup$
– Mostafa Ayaz
Jan 5 at 7:20
2
2
$begingroup$
What is that hard integral? Don't keep it for yourself please :D
$endgroup$
– Zacky
Dec 18 '18 at 21:00
$begingroup$
What is that hard integral? Don't keep it for yourself please :D
$endgroup$
– Zacky
Dec 18 '18 at 21:00
$begingroup$
No closed form as per Wolfram Alpha. How did that sum arise ? What's the integral ?
$endgroup$
– Rebellos
Dec 18 '18 at 21:04
$begingroup$
No closed form as per Wolfram Alpha. How did that sum arise ? What's the integral ?
$endgroup$
– Rebellos
Dec 18 '18 at 21:04
$begingroup$
Check it now it's edited
$endgroup$
– Ahmad Albaw
Dec 18 '18 at 21:11
$begingroup$
Check it now it's edited
$endgroup$
– Ahmad Albaw
Dec 18 '18 at 21:11
$begingroup$
Sorry. Unsolvable........
$endgroup$
– Mostafa Ayaz
Jan 5 at 7:20
$begingroup$
Sorry. Unsolvable........
$endgroup$
– Mostafa Ayaz
Jan 5 at 7:20
add a comment |
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2
$begingroup$
What is that hard integral? Don't keep it for yourself please :D
$endgroup$
– Zacky
Dec 18 '18 at 21:00
$begingroup$
No closed form as per Wolfram Alpha. How did that sum arise ? What's the integral ?
$endgroup$
– Rebellos
Dec 18 '18 at 21:04
$begingroup$
Check it now it's edited
$endgroup$
– Ahmad Albaw
Dec 18 '18 at 21:11
$begingroup$
Sorry. Unsolvable........
$endgroup$
– Mostafa Ayaz
Jan 5 at 7:20