The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A173201

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A173201

Iteration x := x - (sin(x) - cos(x)*x - Pi/2)/(sin(x)*x).
(history; published version)

#37 by Michael De Vlieger at Fri Aug 18 23:51:36 EDT 2023

STATUS

proposed

approved

#36 by Jon E. Schoenfield at Fri Aug 18 23:39:48 EDT 2023

STATUS

editing

proposed

#35 by Jon E. Schoenfield at Fri Aug 18 23:39:47 EDT 2023

NAME

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

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

FORMULA

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

Equals 2*acosarccos(A133731/2).

STATUS

approved

editing

#34 by Charles R Greathouse IV at Wed Mar 03 10:44:25 EST 2021

STATUS

editing

approved

#33 by Charles R Greathouse IV at Wed Mar 03 10:44:21 EST 2021

LINKS

M. Fraser, <a href="http://www.jstor.org/stable/2690163">A tale of two goats</a>, Math. Mag., 55 (1982), 221-227. [From _N. J. A. Sloane_, Jul 12 2011]

#32 by Charles R Greathouse IV at Wed Mar 03 10:37:20 EST 2021

PROG

(PARI) solve(x=1, 2, sin(x)-x*cos(x)-Pi/2) \\ Charles R Greathouse IV, Mar 03 2021

STATUS

approved

editing

#31 by Georg Fischer at Fri Jan 17 03:41:58 EST 2020

STATUS

editing

approved

#30 by Georg Fischer at Fri Jan 17 03:41:53 EST 2020

LINKS

Steven R. Finch, <a href="/A002193/a002193.pdf">Errata and Addenda to Mathematical Constants</a>, January 22, 2016. [Cached copy, with permission of the author]

STATUS

approved

editing

#29 by N. J. A. Sloane at Thu Jan 16 15:19:32 EST 2020

LINKS

Steven R. Finch, <a href="http://www.people.fas.harvardarxiv.edu/~sfinchorg/csolveabs/erradd2001.pdf00578">Errata and Addenda to Mathematical Constants</a>, p. 28.

Discussion

Thu Jan 16

15:19

OEIS Server: https://oeis.org/edit/global/2843

#28 by N. J. A. Sloane at Sun Apr 14 09:45:00 EDT 2019

STATUS

editing

approved