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A195907 Decimal expansion of Sum_{n = -oo..oo} exp(-n^2). 2
1, 7, 7, 2, 6, 3, 7, 2, 0, 4, 8, 2, 6, 6, 5, 2, 1, 5, 3, 0, 3, 1, 2, 5, 0, 5, 5, 1, 1, 5, 7, 8, 5, 8, 4, 8, 1, 3, 4, 3, 3, 8, 6, 0, 4, 5, 3, 7, 2, 2, 4, 6, 0, 5, 3, 8, 3, 1, 5, 9, 0, 5, 1, 0, 8, 7, 9, 9, 6, 8, 6, 8, 0, 8, 3, 9, 6, 3, 4, 0, 1, 2, 5, 4, 0, 3, 3, 8, 7, 1, 7, 4, 2, 4, 9, 6, 0, 0, 2, 9, 6, 4, 0, 5, 1, 9, 0, 7, 1, 3, 4, 7, 3, 5, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A Riemann sum approximation to Integral_{-oo..oo} exp(-x^2) dx = sqrt(Pi).

REFERENCES

Mentioned by N. D. Elkies in a lecture on the Poisson summation formula in Nashville TN in May 2010.

LINKS

Table of n, a(n) for n=1..115.

EXAMPLE

1.77263720482665215303125055115785848134338604537224605383159051...

For comparison, sqrt(Pi) = 1.7724538509055160272981674833411451827975494561223871282138... (A002161).

MATHEMATICA

N[Sum[Exp[-n^2], {n, -Infinity, Infinity}], 200]

RealDigits[ N[ EllipticTheta[3, 0, 1/E], 115]][[1]] (* Jean-François Alcover, Nov 08 2012 *)

PROG

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

CROSSREFS

Cf. A002161, A218792.

Sequence in context: A083871 A255272 A169812 * A126584 A266271 A021568

Adjacent sequences:  A195904 A195905 A195906 * A195908 A195909 A195910

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane, Sep 25 2011

STATUS

approved

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Last modified December 7 08:21 EST 2016. Contains 278849 sequences.