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| bio | website | |
|---|---|---|
| location | ||
| age | ||
| visits | member for | 1 year, 7 months |
| seen | 26 mins ago | |
| stats | profile views | 369 |
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22h |
awarded | Constituent |
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May 12 |
awarded | Caucus |
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Apr 18 |
revised |
Interesting Integral $\int_{-\infty}^{\infty}\frac{e^{i nx}}{\Gamma(\alpha+x) \Gamma(\beta -x)}dx$ added link |
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Apr 18 |
accepted | Non-normalized sinc function |
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Apr 18 |
comment |
Non-normalized sinc function I had hoped there was a faster way but now that I have worked through your proof I doubt it--anything that works might be about this involved. This is a really nice answer and I hope you get more votes for it. |
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Apr 14 |
revised |
Non-normalized sinc function deleted 33 characters in body |
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Apr 14 |
comment |
Generalizing Ramanujan's proof of Bertrand's Postulate: Can Ramanujan's approach be used to show a prime between $4x$ and $5x$ for $x \ge 3$ You might look at the work of Bachraoui and Nagura if you haven't already. We also have a general proof that there is a prime on $(x,(1+1/k)x)$ for large enough x. |
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Apr 14 |
asked | Non-normalized sinc function |
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Apr 7 |
comment |
Understanding Ramanujan's approach in his proof of Bertrand's Postulate +1. i didn't check the stirling approx but plotted the functions. if there's a mistake i don't see it. nice question either way. |
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Apr 7 |
comment |
Understanding Ramanujan's approach in his proof of Bertrand's Postulate We have $\psi(2x)+\psi(2x/2)+\psi(2x/3)...-\psi(x)-\psi(x/2)-\psi(x/3)...$ So $\psi(2x)-\psi(x) < \psi(2x)$ and $\psi(2x/2)-\psi(x/2)< \psi(2x/2)...$ but the sum of these differences could exceed $\psi(2x)$? |
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Apr 5 |
comment |
Dirichlets theorem on primes G.J.O. Jameson's 'The Prime Number Theorem' (Cambridge) is also a good one and it only takes 4 chapters to get the result. Long chapters, though. |
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Apr 4 |
revised |
Discontinuities of $\sum \frac{x^{\rho}}{\rho}$ edited title |
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Mar 31 |
accepted | Discontinuities of $\sum \frac{x^{\rho}}{\rho}$ |
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Mar 31 |
comment |
Discontinuities of $\sum \frac{x^{\rho}}{\rho}$ When you remind me that this expression equals the Chebyshev function it is clear. Thank you! |
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Mar 31 |
revised |
Discontinuities of $\sum \frac{x^{\rho}}{\rho}$ fixed index of second sum |
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Mar 31 |
revised |
Discontinuities of $\sum \frac{x^{\rho}}{\rho}$ clarified behavior of points a bit |
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Mar 30 |
revised |
Discontinuities of $\sum \frac{x^{\rho}}{\rho}$ added 41 characters in body |
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Mar 30 |
revised |
Discontinuities of $\sum \frac{x^{\rho}}{\rho}$ explanation |
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Mar 30 |
revised |
Discontinuities of $\sum \frac{x^{\rho}}{\rho}$ added 24 characters in body |
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Mar 30 |
revised |
Discontinuities of $\sum \frac{x^{\rho}}{\rho}$ added 91 characters in body |
