Hurwitz system

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1: 21.10 Methods of Computation

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Belokolos et al. (1994, Chapter 5) and references therein. Here the Riemann surface is represented by the action of a Schottky group on a region of the complex plane. The same representation is used in Gianni et al. (1998).

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Tretkoff and Tretkoff (1984). Here a Hurwitz system is chosen to represent the Riemann surface.

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2: Bibliography R

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Symbolic and extended-precision general purpose computer algebra system.

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Home Page

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§ ‣ Software Cross Index.

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Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function. Mathematics 9 (16).

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Link, ISSN 2227-7390, Document

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§8.15.

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BibTeX

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Diffraction of plane radio waves by a parabolic cylinder. Calculation of shadows behind hills. Bell System Tech. J. 33, pp. 417–504.

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External Links:

MathReview (J. Shmoys)

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§12.17.

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BibTeX

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Elliptic hypergeometric series on root systems. Adv. Math. 181 (2), pp. 417–447.

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ISSN 0001-8708, Document, MathReview, ZentralBlatt

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§20.11(iii).

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3: Software Index

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	Open Source													With Book						Commercial
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25.21(iv) $\zeta (s,a)$	✓				✓	✓						✓	✓	✓			✓				✓	✓	a
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These are collections of software (e.g. libraries) or interactive systems of a somewhat broad scope. Contents may be adapted from research software or may be contributed by project participants who donate their services to the project. The software is made freely available to the public, typically in source code form. While formal support of the collection may not be provided by its developers, within active projects there is often a core group who donate time to consider bug reports and make updates to the collection.

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4: Bibliography P

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Computer algebra system designed for computations in number theory. Many transcendental functions are also included. PARI is also available as a C library to allow for faster computations. Originally developed by Henri Cohen and co-workers at the Université Bordeaux I.

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Home Page

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

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The Stokes phenomenon associated with the Hurwitz zeta function $\zeta (s,a)$ . Proc. Roy. Soc. London Ser. A 461, pp. 297–304.

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ISSN 1364-5021, Document, MathReview (Marc Prevost), ZentralBlatt

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(25.11.43), §25.11(xii).

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BibTeX

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Systèmes de polynomes biorthogonaux qui généralisent les polynomes ultrasphériques. C. R. Acad. Sci. Paris 228, pp. 1998–2000.

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ISSN 0001-4036, MathReview (G. Szegö)

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§18.35(i).

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BibTeX

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Comoving coordinate system for relativistic hydrodynamics. Phy. Rev. C 75, pp. (024907–1)–(024907–10).

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Document

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§7.21.

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5: Bibliography M

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Some conjectures for root systems. SIAM J. Math. Anal. 13 (6), pp. 988–1007.

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ISSN 0036-1410, Document, MathReview (S. Milne), ZentralBlatt

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§17.13, §17.14.

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BibTeX

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Orthogonal polynomials associated with root systems. Sém. Lothar. Combin. 45, pp. Art. B45a, 40 pp. (electronic).

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ISSN 1286-4889, FullText, MathReview, ZentralBlatt

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§18.37(iii).

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BibTeX

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System for the manipulation of symbolic and numerical expressions. Includes a collection of special functions. Utilizes exact fractions, arbitrary precision integers, and arbitrary precision floating point numbers.

External Links:

Home Page

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

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BibTeX

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Derivatives of the Hurwitz zeta function for rational arguments. J. Comput. Appl. Math. 100 (2), pp. 201–206.

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External Links:

ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

(25.11.21), (25.11.22), (25.11.23), §25.11, §25.11(vi), §25.18(i), (25.6.15).

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BibTeX

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SciFace Software, Paderborn, Germany.

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Notes:

Computer algebra system for doing symbolic and exact algebraic computations as well as numerical calculations with almost arbitrary accuracy

Referenced by:

§ ‣ Software Cross Index.

Encodings:

BibTeX

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