modified Bessel equation
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31—40 of 66 matching pages
31: 13.16 Integral Representations
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13.16.4
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32: 10.56 Generating Functions
33: Bibliography B
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Asymptotic expansions of the modified Bessel function of the third kind of imaginary order.
SIAM J. Appl. Math. 15, pp. 1315–1323.
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Integral representations and summations of the modified Struve function.
Acta Math. Hungar. 141 (3), pp. 254–281.
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Tables of modified Struve functions of orders zero and unity.
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Bessel functions and modular relations of higher type and hyperbolic differential equations.
Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.
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Algorithm 484: Evaluation of the modified Bessel functions K0(Z) and K1(Z) for complex arguments.
Comm. ACM 17 (9), pp. 524–526.
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34: Bibliography S
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A code to evaluate modified Bessel functions based on the continued fraction method.
Comput. Phys. Comm. 105 (2-3), pp. 263–272.
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Bounds for ratios of modified Bessel functions and associated Turán-type inequalities.
J. Math. Anal. Appl. 374 (2), pp. 516–528.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Uniform asymptotic expansions of modified Mathieu functions.
J. Reine Angew. Math. 247, pp. 1–17.
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On the calculation of complex zeros of the modified Bessel function of the second kind.
Dokl. Akad. Nauk SSSR 280 (2), pp. 296–299.
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35: Bibliography P
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On two-sided estimates, uniform with respect to the real argument and index, for modified Bessel functions.
Mat. Zametki 65 (5), pp. 681–692 (Russian).
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Complex zeros of the modified Bessel function
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Math. Comp. 26 (120), pp. 949–953.
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Bounds for ratios of modified Bessel functions.
Integral Transform. Spec. Funct. 9 (4), pp. 293–298.
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Modified Clenshaw-Curtis method for the computation of Bessel function integrals.
BIT 23 (3), pp. 370–381.
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Fast analytic formulas for the modified Bessel functions of imaginary order for spectral line broadening calculations.
J. Quantit. Spec. and Rad. Trans. 62 (4), pp. 389–395.
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36: 18.12 Generating Functions
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18.12.2
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37: 28.28 Integrals, Integral Representations, and Integral Equations
§28.28 Integrals, Integral Representations, and Integral Equations
►§28.28(i) Equations with Elementary Kernels
… ►For details and further equations see Meixner et al. (1980, §2.1.1) and Sips (1970). ►§28.28(ii) Integrals of Products with Bessel Functions
… ►§28.28(v) Compendia
…38: Guide to Searching the DLMF
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►From there you can also access an advanced search page where you can control certain settings, narrowing the search to certain chapters, or restricting the results to equations, graphs, tables, or bibliographic items.
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►Therefore, if your query is
Ai^2+Bi^2
, the system modifies the query so it will find the equations containing the latter expressions.
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►For example, for the Bessel function , you can write K_n(z)
, BesselK_n(z)
, BesselK(n,z)
, or BesselK[n,z]
.
Note that the first form may match other functions than the Bessel
function, so if you are sure you want Bessel
, you might as well enter one of the other 3 forms.
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►For example, you may want equations that contain trigonometric functions, but you don’t care which trigonometric function.
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39: 28.20 Definitions and Basic Properties
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§28.20(i) Modified Mathieu’s Equation
►When is replaced by , (28.2.1) becomes the modified Mathieu’s equation: ►
28.20.1
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