About the Project
NIST

relation to Airy function

AdvancedHelp

(0.007 seconds)

1—10 of 45 matching pages

1: 9.6 Relations to Other Functions
§9.6(i) Airy Functions as Bessel Functions, Hankel Functions, and Modified Bessel Functions
§9.6(ii) Bessel Functions, Hankel Functions, and Modified Bessel Functions as Airy Functions
9.6.20 H 2 / 3 ( 2 ) ( ζ ) = e 2 π i / 3 H - 2 / 3 ( 2 ) ( ζ ) = e - π i / 6 ( 3 / z ) ( Ai ( - z ) + i Bi ( - z ) ) .
§9.6(iii) Airy Functions as Confluent Hypergeometric Functions
2: 13.18 Relations to Other Functions
§13.18(iii) Modified Bessel Functions
3: 36.2 Catastrophes and Canonical Integrals
Ψ 1 is related to the Airy function9.2): … Addendum: For further special cases see §36.2(iv)
4: 13.6 Relations to Other Functions
§13.6(iii) Modified Bessel Functions
5: 9.9 Zeros
§9.9(ii) Relation to Modulus and Phase
6: 9.13 Generalized Airy Functions
Swanson and Headley (1967) define independent solutions A n ( z ) and B n ( z ) of (9.13.1) by …
- A n ( 0 ) = p 1 / 2 B n ( 0 ) = p p Γ ( p ) .
Their relations to the functions A n ( z ) and B n ( z ) are given by …
7: 9.16 Physical Applications
The use of Airy function and related uniform asymptotic techniques to calculate amplitudes of polarized rainbows can be found in Nussenzveig (1992) and Adam (2002). …
8: 9.8 Modulus and Phase
(These definitions of θ ( x ) and ϕ ( x ) differ from Abramowitz and Stegun (1964, Chapter 10), and agree more closely with those used in Miller (1946) and Olver (1997b, Chapter 11).) …
9: Philip J. Davis
After receiving an overview of the project and watching a short demo that included a few preliminary colorful, but static, 3D graphs constructed for the first Chapter, “Airy and Related Functions”, written by Olver, Davis expressed the hope that designing a web-based resource would allow the team to incorporate interesting computer graphics, such as function surfaces that could be rotated and examined. …
10: 10.16 Relations to Other Functions
§10.16 Relations to Other Functions
Elementary Functions
Airy Functions
Parabolic Cylinder Functions
Confluent Hypergeometric Functions