of imaginary argument
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11: 15.19 Methods of Computation
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►For it is possible to use the linear transformations in such a way that the new arguments lie within the unit circle, except when .
This is because the linear transformations map the pair onto itself.
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12: 4.3 Graphics
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§4.3(i) Real Arguments
… ►§4.3(ii) Complex Arguments: Conformal Maps
►Figure 4.3.2 illustrates the conformal mapping of the strip onto the whole -plane cut along the negative real axis, where and (principal value). …Lines parallel to the real axis in the -plane map onto rays in the -plane, and lines parallel to the imaginary axis in the -plane map onto circles centered at the origin in the -plane. … ►§4.3(iii) Complex Arguments: Surfaces
…13: 5.22 Tables
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►This reference also includes for the same arguments to 5D.
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14: Bibliography D
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Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter.
SIAM J. Math. Anal. 21 (4), pp. 995–1018.
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Conical functions of purely imaginary order and argument.
Proc. Roy. Soc. Edinburgh Sect. A 143 (5), pp. 929–955.
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15: Bibliography G
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Algorithm 831: Modified Bessel functions of imaginary order and positive argument.
ACM Trans. Math. Software 30 (2), pp. 159–164.
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Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments.
ACM Trans. Math. Software 30 (2), pp. 145–158.
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16: Software Index
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Open Source | With Book | Commercial | |||||||||||||||||||||||
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10.77(vi) Bessel Functions–Imaginary Order and Real Argument | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||||||||||||||||||
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17: 15.4 Special Cases
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18: 14.20 Conical (or Mehler) Functions
19: 10.61 Definitions and Basic Properties
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►In general, Kelvin functions have a branch point at and functions with arguments
are complex.
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20: 33.11 Asymptotic Expansions for Large
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33.11.4
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