A173201 - OEIS

A173201

Iteration x := x - (sin(x) - cos(x)*x - Pi/2)/(sin(x)*x).

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

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OFFSET

1,2

COMMENTS

Decimal expansion of psi, the unique solution on (0,Pi) of sin(psi) - psi*cos(psi) = Pi/2, an auxiliary constant used in the Hall-Tenenbaum inequality applied to real multiplicative functions. - Jean-François Alcover, Sep 05 2014

LINKS

Table of n, a(n) for n=1..105.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 28.

M. Fraser, A tale of two goats, Math. Mag., 55 (1982), 221-227.

Gerd Lamprecht, Iterationsrechner mit Algorithmus

Gerd Lamprecht, 10000 digits

Gerd Lamprecht, Zahlenfolgen (sequence)

FORMULA

x := x - (sin(x) - cos(x)*x - Pi/2)/(sin(x)*x).

Equals 2*arccos(A133731/2).

EXAMPLE

A133731 = cos(1.9056957293.../2)*2.