of imaginary order
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1: 10.24 Functions of Imaginary Order
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►and , are linearly independent solutions of (10.24.1):
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►In consequence of (10.24.6), when is large and comprise a numerically satisfactory pair of solutions of (10.24.1); compare §2.7(iv).
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►For graphs of and see §10.3(iii).
►For mathematical properties and applications of and , including zeros and uniform asymptotic expansions for large , see Dunster (1990a).
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2: 10.45 Functions of Imaginary Order
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10.45.3
►and , are real and linearly independent solutions of (10.45.1):
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►The corresponding result for is given by
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►For graphs of and see §10.26(iii).
►For properties of and , including uniform asymptotic expansions for large and zeros, see Dunster (1990a).
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3: 10.26 Graphics
4: 10.3 Graphics
5: 10.74 Methods of Computation
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§10.74(viii) Functions of Imaginary Order
►For the computation of the functions and defined by (10.45.2) see Temme (1994c) and Gil et al. (2002d, 2003a, 2004b).6: 10.76 Approximations
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Real Variable; Imaginary Order
…7: 10.77 Software
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§10.77(vi) Bessel Functions–Imaginary Order and Real Argument
…8: 10.75 Tables
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MacDonald (1989) tabulates the first 30 zeros, in ascending order of absolute value in the fourth quadrant, of the function , 6D. (Other zeros of this function can be obtained by reflection in the imaginary axis).
§10.75(viii) Modified Bessel Functions of Imaginary or Complex Order
… ►Žurina and Karmazina (1967) tabulates for , , 7S.
9: Bibliography G
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Evaluation of the modified Bessel function of the third kind of imaginary orders.
J. Comput. Phys. 175 (2), pp. 398–411.
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Computation of the modified Bessel function of the third kind of imaginary orders: Uniform Airy-type asymptotic expansion.
J. Comput. Appl. Math. 153 (1-2), pp. 225–234.
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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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10: 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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