multiplicative functions
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21: 1.10 Functions of a Complex Variable
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►An analytic function
has a zero of order (or multiplicity) () at if the first nonzero coefficient in its Taylor series at is that of .
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►Lastly, if for infinitely many negative , then is an isolated essential singularity.
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22: 13.27 Mathematical Applications
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►Vilenkin (1968, Chapter 8) constructs irreducible representations of this group, in which the diagonal matrices correspond to operators of multiplication by an exponential function.
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23: 27.13 Functions
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►Whereas multiplicative number theory is concerned with functions arising from prime factorization, additive number theory treats functions related to addition of integers.
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24: 18.28 Askey–Wilson Class
25: 27.14 Unrestricted Partitions
26: 31.10 Integral Equations and Representations
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►For suitable choices of the branches of the -symbols in (31.10.9) and the contour , we can obtain both integral equations satisfied by Heun functions, as well as the integral representations of a distinct solution of Heun’s equation in terms of a Heun function (polynomial, path-multiplicative solution).
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27: Bibliography S
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Algorithm 786: Multiple-precision complex arithmetic and functions.
ACM Trans. Math. Software 24 (4), pp. 359–367.
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Algorithm 814: Fortran 90 software for floating-point multiple precision arithmetic, gamma and related functions.
ACM Trans. Math. Software 27 (4), pp. 377–387.
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Efficient multiple-precision evaluation of elementary functions.
Math. Comp. 52 (185), pp. 131–134.
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Algorithm 911: multiple-precision exponential integral and related functions.
ACM Trans. Math. Software 37 (4), pp. Art. 46, 16.
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28: 27.1 Special Notation
29: Bibliography K
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Calculation of the multiple zeros of the derivatives of the cylindrical Bessel functions
and
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Zh. Vychisl. Mat. i Mat. Fiz. 25 (12), pp. 1749–1760, 1918.
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On multiple zeros of derivatives of Bessel’s cylindrical functions.
Dokl. Akad. Nauk SSSR 288 (2), pp. 285–288 (Russian).
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On the calculation of the multiple complex roots of the derivatives of cylindrical Bessel functions.
Zh. Vychisl. Mat. i Mat. Fiz. 27 (11), pp. 1628–1639, 1758.
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Multiple complex zeros of derivatives of the cylindrical Bessel functions.
Dokl. Akad. Nauk SSSR 299 (3), pp. 614–618 (Russian).
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Algorithm 910: a portable C++ multiple-precision system for special-function calculations.
ACM Trans. Math. Software 37 (4), pp. Art. 45, 27.
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