Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



Complex zeros of cylinder functions

Author: Boro Döring
Journal: Math. Comp. 20 (1966), 215-222
MSC: Primary 65.05
MathSciNet review: 0192632
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: All complex zeros of the cylinder functions ${Y_n}(z),{H_n}^{(1)}(z){\text { for }}n = 0$ and $1$, $|z| < 158$, $|\arg z| \leqq \pi$ and some complex zeros small in modulus of ${Y_n}(z)$, ${H_n}^{(1)}(z)$ for $n = 2$, $3$, $4$, $5$, $15$ and $|\arg z| \leqq \pi$ are tabulated accurate to $10D$. The methods (being partly new) for computing these zeros are described.

References [Enhancements On Off] (What's this?)

  • Bessel functions. Part III: Zeros and associated values, Royal Society Mathematical Tables, Vol. 7, Cambridge University Press, New York, 1960. Prepared under the direction of the Bessel Functions Panel of the Mathematical Tables Committee. MR 0119441
  • F. W. J. Olver, The asymptotic expansion of Bessel functions of large order, Philos. Trans. Roy. Soc. London Ser. A 247 (1954), 328–368. MR 67250, DOI
  • Computation Laboratory, National Bureau of Standards, "Tables of the Bessel functions ${Y_0}(z)$ and ${Y_1}(z)$ for complex arguments," Columbia Univ. Press, New York, 1950. MR 12, 285. B. N. Kublanovskaja & T. N. Smirnova, "Zeros of Hankel functions and some related functions," Trudy Mat. Inst. Steklov, v. 53, 1959, pp. 186–191. (Russian) MR 22 #1105.
  • G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR 0010746
  • B. Döring, "Nullstellen von Zylinderfunktionen und verwandten Funktionen. Verfahren zur Bestimmung und Fehlerabschätzung," Thesis, Darmstadt, 1964.
  • J. C. P. Miller, The Airy Integral, Giving Tables of Solutions of the Differential Equation $y”=xy$, Cambridge, at the University Press; New York, The Macmillan Company, 1946. MR 0018971
  • Boro Döring, Inverse Interpolation bei den speziellen Funktionen der mathematischen Physik, Numer. Math. 8 (1966), 123–136 (German). MR 208806, DOI
  • J. C. P. Miller and C. W. Jones, Notes on the evaluation of zeros and turning values of Bessel functions. IV. A new expansion, Philos. Mag. (7) 36 (1945), 200–206. MR 12905

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.05

Retrieve articles in all journals with MSC: 65.05

Additional Information

Article copyright: © Copyright 1966 American Mathematical Society