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1: 20 Theta Functions
Chapter 20 Theta Functions
2: 8 Incomplete Gamma and Related
Functions
3: Sidebar 9.SB2: Interference Patterns in Caustics
The oscillating intensity of the interference fringes across the caustic is described by the Airy function.
4: William P. Reinhardt
His undergraduate and graduate degrees are from the University of California at Berkeley and Harvard University, respectively. …Reinhardt is a frequent visitor to the NIST Physics Laboratory in Gaithersburg, and to the Joint Quantum Institute (JQI) and Institute for Physical Sciences and Technology (ISTP) at the University of Maryland. … Reinhardt was elected to Fellowship in: The American Physical Society 1980, the American Association for the Advancement of Science 1983, Phi Beta Kappa 1998, and The Institute of Physics (UK) 2000. …
  • In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
    5: 36.5 Stokes Sets
    Stokes sets are surfaces (codimension one) in 𝐱 space, across which Ψ K ( 𝐱 ; k ) or Ψ ( U ) ( 𝐱 ; k ) acquires an exponentially-small asymptotic contribution (in k ), associated with a complex critical point of Φ K or Φ ( U ) . …
    36.5.4 80 x 5 40 x 4 55 x 3 + 5 x 2 + 20 x 1 = 0 ,
    36.5.7 X = 9 20 + 20 u 4 Y 2 20 u 2 + 6 u 2 sign ( z ) ,
    6: Sidebar 9.SB1: Supernumerary Rainbows
    For each color, the intensity profile across the rainbow is an Airy function. …
    7: 27 Functions of Number Theory
    8: 28 Mathieu Functions and Hill’s Equation
    9: 8.26 Tables
  • Khamis (1965) tabulates P ( a , x ) for a = 0.05 ( .05 ) 10 ( .1 ) 20 ( .25 ) 70 , 0.0001 x 250 to 10D.

  • Abramowitz and Stegun (1964, pp. 245–248) tabulates E n ( x ) for n = 2 , 3 , 4 , 10 , 20 , x = 0 ( .01 ) 2 to 7D; also ( x + n ) e x E n ( x ) for n = 2 , 3 , 4 , 10 , 20 , x 1 = 0 ( .01 ) 0.1 ( .05 ) 0.5 to 6S.

  • Pagurova (1961) tabulates E n ( x ) for n = 0 ( 1 ) 20 , x = 0 ( .01 ) 2 ( .1 ) 10 to 4-9S; e x E n ( x ) for n = 2 ( 1 ) 10 , x = 10 ( .1 ) 20 to 7D; e x E p ( x ) for p = 0 ( .1 ) 1 , x = 0.01 ( .01 ) 7 ( .05 ) 12 ( .1 ) 20 to 7S or 7D.

  • Zhang and Jin (1996, Table 19.1) tabulates E n ( x ) for n = 1 , 2 , 3 , 5 , 10 , 15 , 20 , x = 0 ( .1 ) 1 , 1.5 , 2 , 3 , 5 , 10 , 20 , 30 , 50 , 100 to 7D or 8S.

  • 10: 23 Weierstrass Elliptic and Modular
    Functions