Bibliography for Airy Functions

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  1. On an Airy function of two variables
    Miyamoto, Tadashi   
    Nonlinear Analysis, Theory, Methods and Applications, v 54, n 4, August, 2003, p 755-772, Compendex.
  2. Some integrals involving airy functions and Volterra µ-functions.
    Vallée, Olivier
    Integral Transforms Spec. Funct. 13 (2002), no. 5, 403--408, MathSciNet.  
  3. Symbolic evaluation of coefficients in Airy-type asymptotic expansions.
    Vidunas, Raimundas; Temme, Nico M.
    Journal of Mathematical Analysis and Applications, May 2002, vol. 269, no. 1, pp. 317-331(15), MathSciNet.  
  4. Analytic variations on the Airy distribution.
    Flajolet, P.; Louchard, G.
    Mathematical analysis of algorithms. Algorithmica 31 (2001), no. 3, 361--377, MathSciNet.  
  5. On nonoscillating integrals for computing inhomogeneous Airy functions.
    Gil, Amparo; Segura, Javier; Temme, Nico M.
    Math. Comp. 70 (2001), no. 235, 1183--1194 (electronic), MathSciNet.  
  6. One-mode model and Airy-like formulae for one-dimensional metallic gratings
    Lalanne P.; Hugonin J.P.; Astilean S.; Palamaru M.; Möller K.D.
    Journal of Optics A: Pure and Applied Optics, 2000, vol. 2, no. 1, pp. 48-51(4), Ingenta.
  7. On the existence of the Airy function in Lipschitz domains. Application to the traces of H2.
    Geymonat, Giuseppe; Krasucki, Françoise
    Comptes Rendus de l'Academie des Sciences Series I Mathematics, 1 March 2000, vol. 330, no. 5, pp. 355-360(6), MathSciNet.  
  8. The method of Airy averaging and some useful applications.
    Arrighini, G. P.; Durante, N.; Guidotti, C.
    J. Math. Chem. 25 (1999), no. 1, 93--103, MathSciNet.  
  9. Airy functions in the thermodynamic Bethe ansatz.
    Fendley, Paul
    Letters in Mathematical Physics, August 1999, vol. 49, no. 3, pp. 229-233(5), MathSciNet.  
  10. The generalized Airy functions.
    Shi, Yuming; Han, Zhenlai; Zhu, Dongmei
    Ann. Differential Equations 14 (1998), no. 2, 287--294, MathSciNet.  
  11. On the Pratt and Airy models of isostatic geoid undulations
    Sjoberg L.E.
    Journal of Geodynamics, September 1998, vol. 26, no. 1, pp. 137-147(11), Ingenta.
  12. An integral representation for the product of Airy functions.
    Vallée, Olivier; Soares, Manuel; de Izarra, Charles
    Z. Angew. Math. Phys. 48 (1997), no. 1, 156--160, MathSciNet.  
  13. A new look at the Airy equation with fences and funnels.
    Hubbard, John H.; McDill, Jean Marie; Noonburg, Anne; West, Beverly H.
    Organic mathematics (Burnaby, BC, 1995), 277--303, CMS Conf. Proc., 20, Amer. Math. Soc., Providence, RI, 1997, MathSciNet.  
  14. Locating and computing zeros of airy functions
    Vrahatis, M.N.; Ragos, O.; Zafiropoulos, F.A.; Grapsa, T.N.  
    Zeitschrift fuer Angewandte Mathematik und Mechanik, ZAMM, Applied Mathematics and Mechanics, v 76, n 7, 1996, p 419, Compendex.
  15. A nonlinear Airy equation.
    Martel, Yvan
    Mat. Apl. Comput. 15 (1996), no. 1, 1--17, MathSciNet.  
  16. Double scaling limits and Airy functions from quasihomogeneous singularities of vector sigma models.
    Rühl, W.
    Modern Phys. Lett. A 10 (1995), no. 31, 2353--2365, MathSciNet.  
  17. Integral representations for products of Airy functions.
    Reid, W. H.
    Z. Angew. Math. Phys. 46 (1995), no. 2, 159--170, MathSciNet.  
  18. On the Airy equation with a coefficient depending on t.
    Popiolek, J.
    Elliptic and parabolic problems (Pont-à-Mousson, 1994), 152--163, Pitman Res. Notes Math. Ser., 325, Longman Sci. Tech., Harlow, 1995, MathSciNet.  
  19. A New Look at the Airy Equation with Fences and Funnels  
    John Hubbard, Jean Marie McDill, Virginia Anne Noonburg, Beverly Henderson West  
    College Math Journal: Volume 25, Number 5, 1994, Pages: 419-431, Jstor.
  20. Longitudinal caustic scale and boundaries of applicability of uniform Airy-asymptotics.
    Asatryan, A. A.; Kravtsov, Yu. A.
    Wave Motion 19 (1994), no. 1, 1--10, MathSciNet.
  21. A Generalization of the Airy Integral for f" - z^n f = 0  
    Gary G. Gundersen, Enid M. Steinbart
    Transactions of the American Mathematical Society, Vol. 337, No. 2. (Jun., 1993), pp. 737-755, Jstor.  
  22. The Laplace transforms of products of Airy functions.
    Shawagfeh, N. T.
    Dirasat Ser. B Pure Appl. Sci. 19 (1992), no. 2, 7--11, MathSciNet.  
  23. Transition from Airy stress function to state space formulation of elasticity.
    Sosa, Horacio A.; Bahar, Leon Y.
    J. Franklin Inst. 329 (1992), no. 5, 817--828, MathSciNet
  24. A Two-Point Boundary Problem for Airy Functions: Problem 90-13 (in Solutions)  
    C. C. Grosjean, H. de Meyer  
    SIAM Review, Vol. 33, No. 3. (Sep., 1991), pp. 477-479, Jstor.  
  25. Generalized symmetries for a Fokker-Planck equation with potential depending on the Airy functions. (Spanish)
    Pérez Cuéllar, A.; Gandarias-Núñez, M. L.; Ramírez-Labrador, J.
    Proceedings of the XII Congress on Differential Equations and Applications/II Congress on Applied Mathematics (Spanish) (Oviedo, 1991), 275--280, Univ. Oviedo, Oviedo, 1991, MathSciNet.  
  26. Linear dispersive equations of Airy type.
    Craig, Walter; Goodman, Jonathan
    J. Differential Equations 87 (1990), no. 1, 38--61, MathSciNet.  
  27. A Riccati approach to the Airy equation.
    Smith, Donald R.
    Asymptotic and computational analysis (Winnipeg, MB, 1989), 403--415, Lecture Notes in Pure and Appl. Math., 124, Dekker, New York, 1990, MathSciNet.  
  28. The Airy Transform  
    D. V. Widder  
    American Mathematical Monthly, Vol. 86, No. 4. (Apr., 1979), pp. 271-277, Jstor.  
  29. Tables of Weyl Fractional Integrals for the Airy Function  
    N. L. Balazs, H. C. Pauli, O. B. Dabbousi  
    Mathematics of Computation, Vol. 33, No. 145. (Jan., 1979), pp. 353-358+s1-s9, Jstor.  
  30. A Dispersion Analysis for Difference Schemes: Tables of Generalized Airy Functions  
    R. C. Y. Chin, G. W. Hedstrom  
    Mathematics of Computation, Vol. 32, No. 144. (Oct., 1978), pp. 1163-1170+s51-s208, Jstor.  
  31. Airy functions in the air: an easy way with stress problems (teaching)
    Frank F.C.
    Physics Education, 1978, vol. 13, no. 4, pp. 258-263(6), Ingenta.
  32. On the Distribution of the Zeros of Generalized Airy Functions  
    V. B. Headley, V. K. Barwell  
    Mathematics of Computation, Vol. 29, No. 131. (Jul., 1975), pp. 863-877, Jstor.  
  33. Problem 72-21, Laplace Transforms of Airy Functions (in Problems)  
    P. Smith  
    SIAM Review, Vol. 14, No. 4. (Oct., 1972), p. 644, Jstor.  
  34. An Extension of Airy's Equation  
    C. A. Swanson, V. B. Headley  
    SIAM Journal on Applied Mathematics, Vol. 15, No. 6. (Nov., 1967), pp. 1400-1412, Jstor.  
  35. Gaussian Quadrature of Some Integrals Involving Airy Functions  
    J. A. Riley, C. Billings  
    Mathematical Tables and Other Aids to Computation, Vol. 13, No. 66. (Apr., 1959), pp. 97-101, Jstor.  
  36. On the Integrability of Certain Partial Differential Equations Proposed by Mr. Airy. [Abstract]  
    R. Moon  
    Proceedings of the Royal Society of London, Vol. 15. (1866 - 1867), pp. 486-489, Jstor.  
  37. Sir George Biddell Airy  
    Geo. A. Hill  
    Science, Vol. 19, No. 469. (Jan. 29, 1892), pp. 64-65, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004