polygamma%20functions
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1: 5.22 Tables
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§5.22(ii) Real Variables
►Abramowitz and Stegun (1964, Chapter 6) tabulates , , , and for to 10D; and for to 10D; , , , , , , , and for to 8–11S; for to 20S. … ►§5.22(iii) Complex Variables
…2: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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Polygamma functions of negative order.
J. Comput. Appl. Math. 100 (2), pp. 191–199.
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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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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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3: Software Index
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►‘✓’ indicates that a software package implements the functions in a section; ‘a’ indicates available functionality through optional or add-on packages; an empty space indicates no known support.
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►In the list below we identify four main sources of software for computing special functions.
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Commercial Software.
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►The following are web-based software repositories with significant holdings in the area of special functions.
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Open Source | With Book | Commercial | |||||||||||||||||||||||
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20 Theta Functions | |||||||||||||||||||||||||
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Such software ranges from a collection of reusable software parts (e.g., a library) to fully functional interactive computing environments with an associated computing language. Such software is usually professionally developed, tested, and maintained to high standards. It is available for purchase, often with accompanying updates and consulting support.
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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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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Calculation of complex polygamma functions.
Sci. Rep. Hirosaki Univ. 43 (1), pp. 161–183.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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5: Bibliography B
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A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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A short table of the functions
, from to
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Phil. Mag. Series 7 20, pp. 343–347.
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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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Computation of the polygamma functions.
Comm. Statist. B—Simulation Comput. 13 (3), pp. 409–415.
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