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1: 10.73 Physical Applications
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§10.73(i) Bessel and Modified Bessel Functions
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…2: Bibliography O
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Studies on the Painlevé equations. I. Sixth Painlevé equation
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Ann. Mat. Pura Appl. (4) 146, pp. 337–381.
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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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.
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Formulae and Tables, The Modified Quotients of Cylinder Functions.
Technical report
Technical Report UDC 517.564.3:518.25, Vol. 4, Report of the Institute of Industrial Science, University of Tokyo, Institute of Industrial Science, Chiba City, Japan.
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Modified quotients of cylinder functions.
Math. Tables Aids Comput. 10, pp. 27–28.
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3: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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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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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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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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4: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Calculation of modified Bessel functions in a complex domain.
Zh. Vychisl. Mat. i Mat. Fiz. 24 (5), pp. 650–664.
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Calculation of the complex zeros of the modified Bessel function of the second kind and its derivatives.
Zh. Vychisl. Mat. i Mat. Fiz. 24 (8), pp. 1150–1163.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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5: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Hill’s Equation.
Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons, New York-London-Sydney.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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6: Bibliography C
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On Temme’s algorithm for the modified Bessel function of the third kind.
ACM Trans. Math. Software 6 (4), pp. 581–586.
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Incomplete Hankel and modified Bessel functions: A class of special functions for electromagnetics.
IEEE Trans. Antennas and Propagation 52 (12), pp. 3373–3389.
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Algorithm 597: Sequence of modified Bessel functions of the first kind.
ACM Trans. Math. Software 9 (2), pp. 242–245.
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Derivatives with respect to the degree and order of associated Legendre functions for using modified Bessel functions.
Integral Transforms Spec. Funct. 21 (7-8), pp. 581–588.
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Coulomb effects in the Klein-Gordon equation for pions.
Phys. Rev. C 20 (2), pp. 696–704.
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7: Bibliography G
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Inequalities for modified Bessel functions and their integrals.
J. Math. Anal. Appl. 420 (1), pp. 373–386.
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On the computation of modified Bessel function ratios.
Math. Comp. 32 (143), pp. 865–875.
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Some integrals involving three modified Bessel functions. I.
J. Math. Phys. 27 (3), pp. 682–687.
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Some integrals involving three modified Bessel functions. II.
J. Math. Phys. 27 (3), pp. 688–695.
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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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8: Bibliography
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Asymptotics of solutions of the generalized sine-Gordon equation, the third Painlevé equation and the d’Alembert equation.
Dokl. Akad. Nauk SSSR 280 (2), pp. 265–268 (Russian).
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Computation of modified Bessel functions and their ratios.
Math. Comp. 28 (125), pp. 239–251.
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Repeated integrals and derivatives of
Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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9: Bibliography P
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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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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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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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10: Bibliography R
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Tablitsy modifitsirovannykh funktsii Besselya
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“Nauka”, Moscow (Russian).
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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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Applied Bessel Functions.
Dover Publications Inc., New York.
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Asymptotics and Bounds of the Roots of Equations (Russian).
Zinatne, Riga.
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Partial fractions expansions and identities for products of Bessel functions.
J. Math. Phys. 46 (4), pp. 043509–1–043509–18.
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