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1: 28.5 Second Solutions fe n , ge n
Second solutions of (28.2.1) are given by … …
Odd Second Solutions
Even Second Solutions
2: 29.17 Other Solutions
§29.17(i) Second Solution
If (29.2.1) admits a Lamé polynomial solution E , then a second linearly independent solution F is given by …
3: 9.15 Mathematical Applications
Airy functions play an indispensable role in the construction of uniform asymptotic expansions for contour integrals with coalescing saddle points, and for solutions of linear second-order ordinary differential equations with a simple turning point. …
4: Bibliography O
  • A. B. Olde Daalhuis and F. W. J. Olver (1995a) Hyperasymptotic solutions of second-order linear differential equations. I. Methods Appl. Anal. 2 (2), pp. 173–197.
  • A. B. Olde Daalhuis (1995) Hyperasymptotic solutions of second-order linear differential equations. II. Methods Appl. Anal. 2 (2), pp. 198–211.
  • F. W. J. Olver (1950) A new method for the evaluation of zeros of Bessel functions and of other solutions of second-order differential equations. Proc. Cambridge Philos. Soc. 46 (4), pp. 570–580.
  • F. W. J. Olver (1967a) Numerical solution of second-order linear difference equations. J. Res. Nat. Bur. Standards Sect. B 71B, pp. 111–129.
  • F. W. J. Olver (1967b) Bounds for the solutions of second-order linear difference equations. J. Res. Nat. Bur. Standards Sect. B 71B (4), pp. 161–166.
  • 5: 28.1 Special Notation
    ce ν ( z , q ) , se ν ( z , q ) , fe n ( z , q ) , ge n ( z , q ) , me ν ( z , q ) ,
    6: 10.25 Definitions
    The defining property of the second standard solution K ν ( z ) of (10.25.1) is …
    7: 28.22 Connection Formulas
    8: Bibliography Y
  • A. I. Yablonskiĭ (1959) On rational solutions of the second Painlevé equation. Vesti Akad. Navuk. BSSR Ser. Fiz. Tkh. Nauk. 3, pp. 30–35 (Russian).
  • 9: Bibliography Z
  • J. M. Zhang, X. C. Li, and C. K. Qu (1996) Error bounds for asymptotic solutions of second-order linear difference equations. J. Comput. Appl. Math. 71 (2), pp. 191–212.
  • 10: 36.5 Stokes Sets
    For | Y | > Y 1 the second sheet is generated by a second solution of (36.5.6)–(36.5.9), and for | Y | < Y 1 it is generated by the roots of the polynomial equation …