The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A032803

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A032803

Expansion of Sum_{i>=0} q^i*theta_3^i.
(history; published version)

#14 by Sean A. Irvine at Tue Jul 08 19:42:19 EDT 2025

STATUS

editing

approved

#13 by Sean A. Irvine at Tue Jul 08 19:42:17 EDT 2025

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#12 by Vaclav Kotesovec at Fri Jun 26 03:31:29 EDT 2020

STATUS

editing

approved

#11 by Vaclav Kotesovec at Fri Jun 26 03:30:36 EDT 2020

MATHEMATICA

nmax = 50; CoefficientList[Series[Sum[x^k*EllipticTheta[3, x]^k, {k, 0, nmax}], {x, 0, nmax}], x] (* _or *) nmax = 50; CoefficientList[Series[1/(1 - x*EllipticTheta[3, x]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 26 2020 *)

#10 by Vaclav Kotesovec at Fri Jun 26 03:21:27 EDT 2020

FORMULA

From Vaclav Kotesovec, Jun 26 2020: (Start)

G.f.: 1/(1 - x*EllipticTheta(3,x)).

a(n) ~ c / r^n, where r = 0.48198821952392600540358080089338068467918852426... is the root of the equation r*EllipticTheta(3,r) = 1 and c = 1 / (1 + r^2 * EllipticTheta'(3,r)) = 0.59345908175794984247602713305661895068944878811545062...

(End)

STATUS

approved

editing

#9 by Vaclav Kotesovec at Fri Jun 26 02:48:14 EDT 2020

STATUS

editing

approved

#8 by Vaclav Kotesovec at Fri Jun 26 02:47:55 EDT 2020

MATHEMATICA

nmax = 50; CoefficientList[Series[Sum[x^k*EllipticTheta[3, x]^k, {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 26 2020 *)

STATUS

approved

editing

#7 by Vaclav Kotesovec at Fri Jun 26 02:46:17 EDT 2020

STATUS

reviewed

approved

#6 by Michel Marcus at Fri Jun 26 00:25:31 EDT 2020

STATUS

proposed

reviewed

Discussion

Fri Jun 26

02:45

Vaclav Kotesovec: From CoefficientList[ Series[Sum[x^k*EllipticTheta[3, x]^k, {k, 0, 20}], {x, 0, 50}], x] I get {1, 1, 3, 5, 11, 23, 47, 99, 203, 423, 877, 1819, 3777, 7831, 16253, 33715, 69953, 145137, 301113, 624745, 1296165, 2689220, 5579382, ... so a(n) for n>=21 is different. What is the problem ?

02:46

Vaclav Kotesovec: Sorry, my mistake. CoefficientList[ Series[Sum[x^k*EllipticTheta[3, x]^k, {k, 0, 50}], {x, 0, 50}], x] is correct.

#5 by Sean A. Irvine at Fri Jun 26 00:23:46 EDT 2020

STATUS

editing

proposed