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modified Bessel equation

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1: 10.25 Definitions
§10.25(i) Modified Bessel’s Equation
§10.25(ii) Standard Solutions
§10.25(iii) Numerically Satisfactory Pairs of Solutions
Table 10.25.1: Numerically satisfactory pairs of solutions of the modified Bessel’s equation.
Pair Region
2: 10.36 Other Differential Equations
§10.36 Other Differential Equations
3: 10.72 Mathematical Applications
§10.72(i) Differential Equations with Turning Points
Bessel functions and modified Bessel functions are often used as approximants in the construction of uniform asymptotic approximations and expansions for solutions of linear second-order differential equations containing a parameter. …
4: 10.73 Physical Applications
10.73.3 4 W + λ 2 2 W t 2 = 0 .
5: 11.2 Definitions
§11.2(ii) Differential Equations
Modified Struve’s Equation
6: 11.9 Lommel Functions
For uniform asymptotic expansions, for large ν and fixed μ = - 1 , 0 , 1 , 2 , , of solutions of the inhomogeneous modified Bessel differential equation that corresponds to (11.9.1) see Olver (1997b, pp. 388–390). … …
7: 10.45 Functions of Imaginary Order
With z = x , and ν replaced by i ν , the modified Bessel’s equation (10.25.1) becomes …
8: Bibliography G
  • A. Gil, J. Segura, and N. M. Temme (2004b) Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments. ACM Trans. Math. Software 30 (2), pp. 145–158.
  • 9: 9.13 Generalized Airy Functions
    and 𝒵 p is any linear combination of the modified Bessel functions I p and e p π i K p 10.25(ii)). Swanson and Headley (1967) define independent solutions A n ( z ) and B n ( z ) of (9.13.1) by …
    10: 10.1 Special Notation
    For older notations see British Association for the Advancement of Science (1937, pp. xix–xx) and Watson (1944, Chapters 1–3).