A087198 - OEIS

A087198

Decimal expansion of 1/(2*sqrt(Pi)).

2, 8, 2, 0, 9, 4, 7, 9, 1, 7, 7, 3, 8, 7, 8, 1, 4, 3, 4, 7, 4, 0, 3, 9, 7, 2, 5, 7, 8, 0, 3, 8, 6, 2, 9, 2, 9, 2, 2, 0, 2, 5, 3, 1, 4, 6, 6, 4, 4, 9, 9, 4, 2, 8, 4, 2, 2, 0, 4, 2, 8, 6, 0, 8, 5, 5, 3, 2, 1, 2, 3, 4, 2, 2, 0, 7, 4, 6, 7, 0, 7, 2, 4, 3, 3, 7, 1, 8, 3, 0, 1, 0, 1, 0, 5, 3, 6, 8, 1, 7, 2, 1, 5, 1, 4

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OFFSET

0,1

COMMENTS

Radius of a sphere with surface area 1.

According to Fouad (2004), to simulate the distance of a sound source under free field conditions, one can multiply "the waveform directly by a gain factor that is the square root of the intensity," which can be computed with the formula D = sqrt(1/(4 * Pi * d^2)) = 1/(3.55 * d), where d is the distance between the sound source and the listener and 3.55 is approximately 10(sqrt(Pi)/5) (A019707) (equation 15 in the chapter), though "in practice we usually drop the constant multiplier" (4 * Pi). If the distance is one unit, then D works out to this number. - Alonso del Arte, Jun 10 2012

REFERENCES

Hesham Fouad, "Spatialization with Stereo Loudspeakers: Understanding Balance, Panning and Distance Attenuation" in Audio Anecdotes II: Tools, Tips, and Techniques for Digital Audio, K. Greenebaum & R. Barzel, eds. Wellesley, Massachusetts: A K Peters (2004): 150 - 153

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Index entries for transcendental numbers

FORMULA

1/(2 * sqrt(Pi)) = sqrt(1/(4 * Pi)).

EXAMPLE

0.28209479177387814347...

MATHEMATICA

RealDigits[Sqrt[1/(4Pi)], 10, 100][[1]] (* Alonso del Arte, Jun 10 2012 *)

PROG

(PARI) sqrt(1/(4*Pi)) \\ G. C. Greubel, Jan 09 2017

CROSSREFS