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Revision History for A122857

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A122857

Expansion of (phi(q)^2 + phi(q^3)^2) / 2 in powers of q where phi() is a Ramanujan theta function.
(history; published version)

#29 by Michael De Vlieger at Tue Nov 21 08:32:39 EST 2023

STATUS

reviewed

approved

#28 by Joerg Arndt at Tue Nov 21 04:01:06 EST 2023

STATUS

proposed

reviewed

#27 by Amiram Eldar at Tue Nov 21 00:54:23 EST 2023

STATUS

editing

proposed

#26 by Amiram Eldar at Tue Nov 21 00:53:03 EST 2023

KEYWORD

nonn,easy,changed

#25 by Amiram Eldar at Tue Nov 21 00:08:50 EST 2023

FORMULA

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*Pi/3 = 2.0943951... (A019693). - _Amiram Eldar_, Nov 21 2023

#24 by Amiram Eldar at Tue Nov 21 00:08:32 EST 2023

LINKS

Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>, 2019.

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>.

FORMULA

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*Pi/3 = 2.0943951... (A019693).

CROSSREFS

Cf. A002654, A008441, A019693, A035154, A113446, A125079, A125061, A132003.

Cf. A000122, A000700, A010054, A121373.

STATUS

approved

editing

#23 by N. J. A. Sloane at Tue Mar 14 09:33:36 EDT 2023

STATUS

proposed

approved

#22 by Michel Marcus at Mon Mar 06 01:35:24 EST 2023

STATUS

editing

proposed

#21 by Michel Marcus at Mon Mar 06 01:35:20 EST 2023

FORMULA

a(n) = (-1)^n * A132003(n). Expansion of (phi(-q^3) / phi(-q)) * phi(-q^2) * phi(-q^6) in powers of q where phi() is a Ramanujan theta function. - _Michael Somos_, Mar 05 2023

- Michael Somos, Mar 05 2023

STATUS

proposed

editing

#20 by Michael Somos at Sun Mar 05 19:00:09 EST 2023

STATUS

editing

proposed