Timeline for Does $\prod_{k=1}^\infty\left[1-\big((k+1)^{1/3}-k^{1/3}\big)^3\right]$ have a closed form?
Current License: CC BY-SA 4.0
9 events
when toggle format | what | by | license | comment | |
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May 17 at 9:22 | comment | added | Dan | @MaxMuller Yes, I did. Unfortunately it didn't help. | |
May 17 at 9:10 | comment | added | Max Lonysa Muller | @Dandif you check the OEIS? | |
May 17 at 3:45 | history | edited | Dan | CC BY-SA 4.0 |
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May 17 at 0:34 | comment | added | user491858 | @mathworker21 It is very much a different (and easier) question to say that a function does not have a closed form. Proving that $\log(x)$ is a transcendental function over $\mathbf{Q}(x)$ is easy. Proving that $\log(-1) = \pi i$ is transcendental is harder. | |
May 17 at 0:10 | comment | added | mathworker21 | @user491858 Isn't there a whole theory that is able to say, e.g., $\int e^{-x^2}dx$ does not have a "closed form"? | |
May 16 at 22:39 | comment | added | Dan | @user491858 If no one here provides a closed form, I'll assume that it probably doesn't have a closed form. | |
May 16 at 22:38 | comment | added | user491858 | Do you want an answer beyond "obviously not"? Proving that something doesn't have a closed form is close to impossible. I don't even know how to prove that $\sum_{k=1}^{\infty} 1/k^5$ doesn't have a closed form as a rational number. | |
May 16 at 22:33 | history | edited | Dan | CC BY-SA 4.0 |
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May 16 at 22:20 | history | asked | Dan | CC BY-SA 4.0 |