Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Complex roots of $\textrm {sin}$ $z=az,$ $\textrm {cos}$ $z=az,$ and $\textrm {cosh}$ $z=az$
HTML articles powered by AMS MathViewer

by Henry E. Fettis PDF
Math. Comp. 30 (1976), 541-545 Request permission

Abstract:

Values of the first five complex roots of the equations $\sin z = az,\cos z = az$ and $\cosh z = az$ are given to 10S, for $a = 10,5,2,1.6,1.2,1(.1).3$, and selected values below.
References
  • A. P. Hillman and H. E. Salzer, Roots of $\sin z=z$, Philos. Mag. (7) 34 (1943), 575. MR 8710
  • J. Fadle, Die Selbstspannungs-Eigenwertfunktionen der quadratischen Scheibe, Ing.-Arch. 11 (1940), 125–149 (German). MR 2307, DOI 10.1007/BF02084699
  • B. S. MITTELMAN & A. P. HILLMAN, "Zeros of $z + \sin z$," MTAC, v. 2, 1947, pp. 60-61.
  • C. I. Robbins and R. C. T. Smith, A table of roots of sin $Z=-Z$, Philos. Mag. (7) 39 (1948), 1004–1005. MR 28667
  • Lelia Ricci, Tavola di radici di basso modulo di un’equazione interessante la scienza delle costruzioni, Consiglio Naz. Ricerche. Pubbl. Ist. Appl. Calcolo 1951 (1951), no.Β 296, 8 (Italian). MR 42776
  • R. M. COGHLAN & R. C. T. SMITH, "Table of roots of $\sin z = kz$," MTAC, v. 5, 1951, p. 231. UMT 131.
  • Chih Bing Ling, Values of roots of eight equations of algebraic-transcendental type, Hung-ching Chow Sixty-fifth Anniversary Volume, Nat. Taiwan Univ., Math. Res. Center, Taipei, 1967, pp.Β 186–195. MR 0225465
  • T. H. MILLER, "On the numerical values of the roots of the equation $\cos x = x$," Proc. Edinburgh Math. Soc., v. 9, 1891, pp. 80-83. L. SILBERSTEIN, "The roots of $\cos z = z$," Philos. Mag., v. 20 (7), 1935, pp. 528-531.
  • Shiu-fong Yeung and Chih Bing Ling, On values of roots of monomial-transcendental equations, Hung-ching Chow Sixty-fifth Anniversary Volume, Nat. Taiwan Univ., Math. Res. Center, Taipei, 1967, pp.Β 196–204. MR 0225466
  • Harold T. Davis and Vera J. Fisher, Tables of the mathematical functions. Vol. III: Arithmetical tables. , The Principia Press of Trinity University, San Antonio, Tex., 1962. MR 0142795
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 65A05
  • Retrieve articles in all journals with MSC: 65A05
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Math. Comp. 30 (1976), 541-545
  • MSC: Primary 65A05
  • DOI: https://doi.org/10.1090/S0025-5718-1976-0418401-9
  • MathSciNet review: 0418401