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A231786 Negative initial slope of the Thomas-Fermi equation, y"(x) = Sqrt( y(x)^3 / x), with boundary conditions y(0) = 1 and y(Infinity) = 0 1
1, 5, 8, 8, 0, 7, 1, 0, 2, 2, 6, 1, 1, 3, 7, 5, 3, 1, 2, 7, 1, 8, 6, 8, 4, 5, 0, 9, 4, 2, 3, 9, 5, 0, 1, 0, 9, 4, 5, 2, 7, 4, 6, 6, 2, 1, 6, 7, 4, 8, 2, 5, 6, 1, 6, 7, 6, 5, 6, 7, 7, 4, 1, 8, 1, 6, 6, 5, 5, 1, 9, 6, 1, 1, 5, 4, 3, 0, 9, 2, 6, 2, 3, 3, 2, 0, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, Springer, 1999, p. 167.

Max Born, Atomic Physics, Blackie & Son Ltd., 8th. ed., 1969, p. 200.

John P. Boyd, Rational Chebyshev series for the Thomas-Fermi function: Endpoint singularities and spectral methods, Journal of Computational and Applied Mathematics, 244 (2013), p. 90-101.

Hagen Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 5th edition, World Scientific (Singapore, 2009), p. 422.

J. Schwinger, Thomas-Fermi model: The Leading correction, Phys. Rev A, vol 22 (1980), p. 1827-1832.

J. Schwinger, Quantum Mechanics: Symbolism of Atomic Measurements, Springer (2001), p. 419.

M. Tavassoli Kajani, A. Kiliçman, and M. Maleki, The Rational Third-Kind Chebyshev Pseudospectral Method for the Solution of the Thomas-Fermi Equation over Infinite Interval, Mathematical Problems in Engineering, Article 537810, (2013).

LINKS

Peter J. C. Moses, Table of n, a(n) for n = 1..5000

P. Amore, J. Boyd, F. Fernández, Accurate calculation of the solutions to the Thomas-Fermi equations

S. Esposito, Majorana solution of the Thomas-Fermi equation, Am. J. Phys. 70 (8), p 852-856. (2002)

R. P. Feynman, N. Metropolis, and E. Teller, Equations of State of Elements Based on the Generalized Fermi-Thomas Theory, Phys. Rev. 75, p 1561-1573 (1949)

MATHEMATICA

nn = 150; Clear[a]; a[0] = 1; a[1] = 9 - Sqrt[73]; (* a[m]:=N[_, x] will give about x/3 digits and will calculate up to about a[4 x]. Example: to find 1000 digits, x needs to be 3000 and will calculate a[m] upto about a[12500] *) a[m_] := a[m] = N[(Sum[((n + 7) a[n - 1] + (n + 1) a[n + 1] - 2 (n + 4) a[n]) a[m - n], {n, m - 2}] + (a[1] (m + 6)) a[m - 2] + ((m + 7) - 2 a[1] (m + 3)) a[m - 1])/(2 (m + 8) - a[1] (m + 1)), nn]; RealDigits[N[(3/16)^(1/3) Sum[a[n], {n, 0, #[[2]]}], #[[1]]] &[{-MantissaExponent[a[#]][[2]] - 1, #} &[NestWhile[# + 1 &, 0, Precision[a[#]] > 5 &] - 1]]][[1]]

CROSSREFS

Sequence in context: A039678 A259234 A131040 * A007450 A303816 A200297

Adjacent sequences:  A231783 A231784 A231785 * A231787 A231788 A231789

KEYWORD

nonn

AUTHOR

Peter J. C. Moses, Nov 13 2013

STATUS

approved

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Last modified April 3 01:50 EDT 2020. Contains 333195 sequences. (Running on oeis4.)