Chapter 12Parabolic Cylinder Functions
N. M. TemmeCentrum voor Wiskunde en Informatica, Department MAS, Amsterdam, The Netherlands.
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- Acknowledgements:
- This chapter is based in part onAbramowitz and Stegun (1964, Chapter 19) by J. C. P. Miller.
- Notes:
- The main references used in writing this chapter areErdélyi et al. (1953b, v. 2),Miller (1955), andOlver (1959). For additional bibliographic reading seeBuchholz (1969),Lebedev (1965),Magnus et al. (1966),Olver (1997b), andTemme (1996b).
- Referenced by:
- §18.15(v),ProfileNico M. Temme,ProfileNico M. Temme,§ ‣Chapter Authors,§ ‣Associate Editors,§ ‣Software Cross Index
- Permalink:
- http://dlmf.nist.gov/12
- Notation
- Properties
- 12.2Differential Equations
- 12.3Graphics
- 12.4Power-Series Expansions
- 12.5Integral Representations
- 12.6Continued Fraction
- 12.7Relations to Other Functions
- 12.8Recurrence Relations and Derivatives
- 12.9Asymptotic Expansions for Large Variable
- 12.10Uniform Asymptotic Expansions for Large Parameter
- 12.11Zeros
- 12.12Integrals
- 12.13Sums
- 12.14The Function
- 12.15Generalized Parabolic Cylinder Functions
