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Search: id:A138282
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| A138282 |
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Decimal expansion of the real part of z0, the smallest nonzero first-quadrant solution of z = Sin(z). |
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+0
2
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| 7, 4, 9, 7, 6, 7, 6, 2, 7, 7, 7, 7, 6, 3, 8, 5, 4, 9, 8, 2, 7, 2, 3, 2, 4, 9, 9, 6, 5, 8, 9, 9, 3, 5, 9, 9, 9, 5, 0, 5, 5, 2, 2, 0, 3, 2, 0, 5, 0, 8, 6, 2, 0, 3, 9, 8, 0, 8, 1, 7, 1, 0, 2, 7, 4, 7, 2, 8, 6, 3, 0, 5, 4, 4, 8, 6, 7, 8, 9, 3, 5, 3, 7, 2, 7, 2, 6, 2, 9, 9, 7, 3, 2, 5, 1, 5, 3, 6, 4, 9, 0, 0, 3, 7, 0
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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z0 is a repelling fixed point of Sin(z). The constant z0 appears in the paper by Shenderov.
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REFERENCES
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E. L. Shenderov, Helmholtz equation solutions corresponding to multiple roots of the dispersion equation for a waveguide with impedance walls (Russian), Acoustical Physics 46 (2000), 357-363.
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EXAMPLE
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7.497676277776385498272325...
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MATHEMATICA
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z0 = FindRoot[{Re[Sin[x+I*y]]==x, Im[Sin[x+I*y]]==y}, {{x, 7}, {y, 3}}, WorkingPrecision->150]; RealDigits[z0[[1, 2]]]
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CROSSREFS
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Cf. A138283 (imaginary part).
Sequence in context: A019795 A110644 A117028 this_sequence A155823 A103227 A165415
Adjacent sequences: A138279 A138280 A138281 this_sequence A138283 A138284 A138285
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KEYWORD
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cons,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Mar 12 2008
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