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Search: id:A138283
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| A138283 |
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Decimal expansion of the imaginary part of z0, the smallest nonzero first-quadrant solution of z = Sin(z). |
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+0
2
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| 2, 7, 6, 8, 6, 7, 8, 2, 8, 2, 9, 8, 7, 3, 2, 1, 5, 3, 2, 4, 9, 5, 3, 1, 3, 9, 1, 3, 0, 5, 1, 4, 0, 9, 0, 2, 0, 7, 1, 5, 5, 5, 1, 6, 5, 9, 0, 0, 0, 8, 6, 5, 6, 7, 4, 7, 3, 1, 3, 0, 3, 8, 4, 2, 8, 4, 8, 0, 2, 6, 7, 1, 4, 2, 7, 6, 9, 6, 3, 8, 1, 3, 0, 8, 4, 8, 0, 1, 6, 0, 3, 8, 0, 8, 1, 7, 0, 2, 4, 3, 0, 5, 8, 5, 6
(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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2.768678282987321532495314...
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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[[2, 2]]]
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CROSSREFS
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Cf. A138282 (real part).
Sequence in context: A103557 A158241 A156591 this_sequence A117968 A154200 A089417
Adjacent sequences: A138280 A138281 A138282 this_sequence A138284 A138285 A138286
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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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