

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
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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]] (* JeanFrançois Alcover, Nov 08 2012 *)


CROSSREFS

Cf. A002161, A218792.
Sequence in context: A002161 A083871 A169812 * A126584 A021568 A199613
Adjacent sequences: A195904 A195905 A195906 * A195908 A195909 A195910


KEYWORD

nonn,cons


AUTHOR

N. J. A. Sloane, Sep 25 2011


STATUS

approved



