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1 - ((sin pi x)/(pi x))^2
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(Redirected from 1 - sinc^2 x)
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The elementary transcendental function
where
is the normalized sinc function.
is the main part of the correlation function in Montgomery's pair correlation conjecture.
Contents
Maclaurin series expansion of 1 - ((sin pi x)/(pi x))^2
The Maclaurin series expansion of 1 - ((sin pi x)/(pi x))^2 is
1 - ((sin x)/x)^2
Maclaurin series expansion of 1 - ((sin x)/x)^2
The Maclaurin series expansion of 1 - ((sin x)/x)^2 is
Numerators of Maclaurin series for 1 - ((sin x)/x)^2
A048896 2 A000120() − 1, . Maximal power of 2 dividing th Catalan number (A000108).
- {1, 2, 1, 2, 2, 4, 1, 2, 2, 4, 2, 4, 4, 8, 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, ...}
A000120 1's-counting sequence: number of 1's in binary expansion of (or the binary weight of ).
- {1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, ...}
Denominators of Maclaurin series for 1 - ((sin x)/x)^2
A117972 Numerator of .
- {3, -45, 315, -14175, 467775, -42567525, 638512875, -97692469875, 9280784638125, -2143861251406875, 147926426347074375, -48076088562799171875, 9086380738369043484375, -3952575621190533915703125, ...}