Modulus and phase of the reduced logarithmic derivative of the cylindrical Bessel function
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- by Andrés Cruz and Javier Sesma PDF
- Math. Comp. 35 (1980), 1317-1324 Request permission
Abstract:
The modulus and phase of the reduced logarithmic derivative of the cylindrical Bessel function \[ z{J\prime _v}(z)/{J_v}(z),\] for complex variable z and real order v, are investigated. Special attention is paid to the location of saddle points and their trajectories as v varies.References
- A. Cruz and J. Sesma, Convergence of the Debye expansion for the $S$ matrix, J. Math. Phys. 20 (1979), no. 1, 126–131. MR 517379, DOI 10.1063/1.523952 M. ABRAMOWITZ & I. A. STEGUN (Editors), Handbook of Mathematical Functions, Dover, New York, 1965.
- Wilhelm Magnus, Fritz Oberhettinger, and Raj Pal Soni, Formulas and theorems for the special functions of mathematical physics, Third enlarged edition, Die Grundlehren der mathematischen Wissenschaften, Band 52, Springer-Verlag New York, Inc., New York, 1966. MR 0232968
- Yudell L. Luke, Mathematical functions and their approximations, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0501762
- Walter Gautschi and Josef Slavik, On the computation of modified Bessel function ratios, Math. Comp. 32 (1978), no. 143, 865–875. MR 470267, DOI 10.1090/S0025-5718-1978-0470267-9
- Henry E. Fettis, James C. Caslin, and Kenneth R. Cramer, Saddle points of the complementary error function, Math. Comp. 27 (1973), 409–412. MR 326992, DOI 10.1090/S0025-5718-1973-0326992-9
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Math. Comp. 35 (1980), 1317-1324
- MSC: Primary 33A40; Secondary 65H05
- DOI: https://doi.org/10.1090/S0025-5718-1980-0583509-5
- MathSciNet review: 583509