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A218792 Decimal expansion of Sum_{n = -oo..oo} e^(-2*n^2). 5
1, 2, 7, 1, 3, 4, 1, 5, 2, 2, 1, 8, 9, 0, 1, 5, 2, 2, 5, 2, 2, 2, 3, 8, 2, 5, 7, 8, 7, 9, 0, 9, 3, 5, 6, 2, 4, 9, 7, 6, 8, 6, 4, 9, 8, 7, 7, 1, 7, 6, 2, 6, 7, 0, 1, 1, 6, 4, 4, 1, 0, 8, 0, 1, 6, 9, 7, 4, 7, 7, 5, 8, 5, 6, 6, 5, 5, 3, 0, 7, 5, 0, 6, 2, 3, 9, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

FORMULA

Equals Jacobi theta_{3}(0,exp(-2)). - G. C. Greubel, Feb 01 2017

EXAMPLE

1.2713415221890152252223825787909356249768649877176...

For comparison, sqrt(Pi/2) = 1.2533141373155002512078826424055226265034933703050...

MATHEMATICA

RealDigits[Sum[E^(-2*k^2), {k, -Infinity, Infinity}], 10, 200][[1]]

RealDigits[EllipticTheta[3, 0, 1/E^2], 10, 200][[1]] (* Vaclav Kotesovec, Sep 22 2013 *)

PROG

(PARI) 1 + 2*suminf(n=1, exp(-2*n^2)) \\ Charles R Greathouse IV, Jun 06 2016

CROSSREFS

Cf. A195907, A069998, A167009, A167010, A229052.

Sequence in context: A324329 A201889 A145057 * A065254 A010592 A096381

Adjacent sequences:  A218789 A218790 A218791 * A218793 A218794 A218795

KEYWORD

nonn,cons

AUTHOR

Vaclav Kotesovec, Nov 05 2012

STATUS

approved

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Last modified February 17 17:59 EST 2020. Contains 331999 sequences. (Running on oeis4.)