representation via Hurwitz system
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1: 25.11 Hurwitz Zeta Function
§25.11 Hurwitz Zeta Function
… ►§25.11(iii) Representations by the Euler–Maclaurin Formula
… ►§25.11(iv) Series Representations
… ►§25.11(vii) Integral Representations
… ►§25.11(x) Further Series Representations
…2: 21.10 Methods of Computation
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Tretkoff and Tretkoff (1984). Here a Hurwitz system is chosen to represent the Riemann surface.
Deconinck and van Hoeij (2001). Here a plane algebraic curve representation of the Riemann surface is used.
3: 8.15 Sums
4: 18.38 Mathematical Applications
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Quadrature
… ►Quadrature “Extended” to Pseudo-Spectral (DVR) Representations of Operators in One and Many Dimensions
►The basic ideas of Gaussian quadrature, and their extensions to non-classical weight functions, and the computation of the corresponding quadrature abscissas and weights, have led to discrete variable representations, or DVRs, of Sturm–Liouville and other differential operators. … ►Group Representations
… ►Algebraic structures were built of which special representations involve Dunkl type operators. …5: Wolter Groenevelt
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►Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems.
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6: Bibliography H
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Lie groups, Lie algebras, and representations.
Second edition, Graduate Texts in Mathematics, Vol. 222, Springer, Cham.
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Analytic evaluation of two-center STO electron repulsion integrals via ellipsoidal expansion.
Internat. J. Quantum Chem. 88 (6), pp. 701–734.
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Numerical Tools for the Study of Finite Gap Solutions of Integrable Systems.
Ph.D. Thesis, Technischen Universität Berlin.
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Sums of powers of integers via generating functions.
Fibonacci Quart. 34 (3), pp. 244–256.
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Bernoulli numbers and polynomials via residues.
J. Number Theory 76 (2), pp. 178–193.
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7: Bibliography K
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Series expansions for the third incomplete elliptic integral via partial fraction decompositions.
J. Comput. Appl. Math. 207 (2), pp. 331–337.
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The congruences of Clausen-von Staudt and Kummer for Bernoulli-Hurwitz numbers.
Math. Ann. 216 (1), pp. 1–4.
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Closed-form representations of the Lambert function.
Fract. Calc. Appl. Anal. 7 (2), pp. 177–190.
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Comment on “The incomplete beta function law for parallel tempering sampling of classical canonical systems” [J. Chem. Phys. 120, 4119 (2004)].
J. Chem. Phys. 121 (2), pp. 1167.
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Compact quantum groups and -special functions.
In Representations of Lie Groups and Quantum Groups,
Pitman Res. Notes Math. Ser., Vol. 311, pp. 46–128.
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8: 9.17 Methods of Computation
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§9.17(iii) Integral Representations
►Among the integral representations of the Airy functions the Stieltjes transform (9.10.18) furnishes a way of computing in the complex plane, once values of this function can be generated on the positive real axis. … ►§9.17(iv) Via Bessel Functions
… ►Zeros of the Airy functions, and their derivatives, can be computed to high precision via Newton’s rule (§3.8(ii)) or Halley’s rule (§3.8(v)), using values supplied by the asymptotic expansions of §9.9(iv) as initial approximations. …9: Bibliography B
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Integral representations and summations of the modified Struve function.
Acta Math. Hungar. 141 (3), pp. 254–281.
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On the Hurwitz zeta-function.
Rocky Mountain J. Math. 2 (1), pp. 151–157.
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A new asymptotic representation for and quantum spectral determinants.
Proc. Roy. Soc. London Ser. A 437, pp. 151–173.
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From Klein to Painlevé via Fourier, Laplace and Jimbo.
Proc. London Math. Soc. (3) 90 (1), pp. 167–208.
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Riemann zeta function: Rapidly converging series and integral representations.
Appl. Math. Lett. 5 (2), pp. 83–88.
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10: Bibliography R
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A non-negative representation of the linearization coefficients of the product of Jacobi polynomials.
Canad. J. Math. 33 (4), pp. 915–928.
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Integral representations for products of Airy functions.
Z. Angew. Math. Phys. 46 (2), pp. 159–170.
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Integral representations for products of Airy functions. II. Cubic products.
Z. Angew. Math. Phys. 48 (4), pp. 646–655.
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Integral representations for products of Airy functions. III. Quartic products.
Z. Angew. Math. Phys. 48 (4), pp. 656–664.
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