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1: Bibliography B

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Algorithms for computing Bessel functions of half-integer order with complex arguments. Zh. Vychisl. Mat. i Mat. Fiz. 28 (10), pp. 1449–1460, 1597.

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Notes:

English translation in U.S.S.R. Comput. Math. and Math. Phys. 28(1988), no. 5, 109–117

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ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.77(iv).

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Algorithms for evaluating spherical Bessel functions in the complex domain. Zh. Vychisl. Mat. i Mat. Fiz. 28 (12), pp. 1779–1788, 1918.

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Notes:

English translation in U.S.S.R. Comput. Math. and Math. Phys. 28(1988), no. 6, 122–128

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ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.77(iv).

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Products of generalized hypergeometric series. Proc. London Math. Soc. (2) 28 (2), pp. 242–254.

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External Links:

Document, ZentralBlatt

Referenced by:

§16.12.

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Transformations of generalized hypergeometric series. Proc. London Math. Soc. (2) 29 (2), pp. 495–502.

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Document, ZentralBlatt

Referenced by:

§16.6.

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Über Sturm-Liouvillesche Polynomsysteme. Math. Z. 29 (1), pp. 730–736.

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External Links:

ISSN 0025-5874, Link, MathReview Entry, ZentralBlatt

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2: Bibliography S

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Numerical evaluation of spherical Bessel transforms via fast Fourier transforms. J. Comput. Phys. 100 (2), pp. 294–296.

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ISSN 0021-9991, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vii).

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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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External Links:

Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§28.8(iv).

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The elliptical microstrip antenna with circular polarization. IEEE Trans. Antennas and Propagation 29 (1), pp. 90–94.

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FullText

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5th item.

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Sturm oscillation and comparison theorems. In Sturm-Liouville theory, pp. 29–43.

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External Links:

Document, Link, MathReview Entry

Referenced by:

§18.36(vi), §18.39(i).

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Text-book on Spherical Astronomy. Fifth edition, Cambridge University Press, Cambridge.

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External Links:

MathReview

Referenced by:

§4.42(iii).

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3: Bibliography

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Asymptotic expansions of spheroidal wave functions. J. Math. Phys. Mass. Inst. Tech. 28, pp. 195–199.

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External Links:

MathReview (J. G. van der Corput), ZentralBlatt

Referenced by:

§30.9(iii).

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Theory of Incomplete Cylindrical Functions and Their Applications. Springer-Verlag, Berlin.

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Notes:

Translated from the Russian by H. E. Fettis, J. W. Goresh and D. A. Lee, Die Grundlehren der mathematischen Wissenschaften, Band 160

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MathReview, ZentralBlatt

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1st item.

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Study of nuclear structure by electromagnetic excitation with accelerated ions. Rev. Mod. Phys. 28, pp. 432–542.

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ISSN 0034-6861, Document, MathReview, ZentralBlatt

Referenced by:

§33.22(ii).

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Computation of modified Bessel functions and their ratios. Math. Comp. 28 (125), pp. 239–251.

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ISSN 0025-5718, FullText, MathReview (L. Lorch), ZentralBlatt

Referenced by:

§10.74(v).

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Normal forms of functions in the neighborhood of degenerate critical points. Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).

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Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiĭ (1901–1973), I. In Russian. English translation: Russian Math. Surveys, 29(1974), no. 2, pp. 10–50.

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Document, MathReview (G. R. Belickii), ZentralBlatt

Referenced by:

§36.2(i).

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4: Software Index

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	Open Source													With Book						Commercial
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10.77(ii) Bessel Functions–Real Argument and Integer or Half-Integer Order (including Spherical Bessel Functions)	✓	✓	✓	✓	✓	✓	✓	✓	✓		✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	FDLIBM, NMS
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20 Theta Functions
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28 Mathieu Functions and Hill’s Equation
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5: Bibliography D

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Sur une classe de nombres rationnels réductibles aux nombres de Bernoulli. Bull. Sci. Math. (2) 28, pp. 29–32 (French).

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External Links:

ZentralBlatt

Referenced by:

§24.1.

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Complex zeros of linear combinations of spherical Bessel functions and their derivatives. SIAM J. Math. Anal. 4 (1), pp. 128–133.

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ISSN 1095-7154, Document, MathReview (C. J. Bouwkamp), ZentralBlatt

Referenced by:

§10.58.

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Computing Riemann matrices of algebraic curves. Phys. D 152/153, pp. 28–46.

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ISSN 0167-2789, Document, MathReview (John B. Little), ZentralBlatt

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3rd item.

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Note on the addition theorem of parabolic cylinder functions. J. Indian Math. Soc. (N. S.) 4, pp. 29–30.

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External Links:

MathReview (M. C. Gray), ZentralBlatt

Referenced by:

§12.13(ii).

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The incomplete beta function—a historical profile. Arch. Hist. Exact Sci. 24 (1), pp. 11–29.

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ISSN 0003-9519, MathReview (Willard Parker), ZentralBlatt

Referenced by:

§8.17(i).

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6: Bibliography G

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A continued fraction algorithm for the computation of higher transcendental functions in the complex plane. Math. Comp. 21 (97), pp. 18–29.

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External Links:

FullText, MathReview (D. C. Gilles), ZentralBlatt

Referenced by:

§10.74(v), §3.10(ii).

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Algorithm 819: AIZ, BIZ: two Fortran 77 routines for the computation of complex Airy functions. ACM Trans. Math. Software 28 (3), pp. 325–336.

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Notes:

Double-precision Fortran, maximum accuracy 18S.

External Links:

ISSN 0098-3500, Document, GAMS (module 819; package TOMS), MathReview Entry, ZentralBlatt

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3rd item.

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Algorithm 822: GIZ, HIZ: two Fortran 77 routines for the computation of complex Scorer functions. ACM Trans. Math. Software 28 (4), pp. 436–447.

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Notes:

Double-precision Fortran, maximum accuracy 18S.

External Links:

ISSN 0098-3500, Document, GAMS (module 822; package TOMS), MathReview Entry, ZentralBlatt

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2nd item.

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Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Notes:

Includes Fortran program claiming 12S accuracy

External Links:

ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt

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3rd item, §10.77(ix).

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On the exceptional zeros of cross-products of derivatives of spherical Bessel functions. Z. Angew. Math. Phys. 36 (3), pp. 491–494.

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External Links:

ISSN 0044-2275, Document, MathReview (B. R. Bhonsle), ZentralBlatt

Referenced by:

§10.58.

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