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1: 8.19 Generalized Exponential Integral

§8.19 Generalized Exponential Integral

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§8.19(ii) Graphics

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§8.19(ix) Inequalities

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§8.19(x) Integrals

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§8.19(xi) Further Generalizations

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2: 16.2 Definition and Analytic Properties

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§16.2(i) Generalized Hypergeometric Series

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Polynomials

… ►Note also that any partial sum of the generalized hypergeometric series can be represented as a generalized hypergeometric function via … ►

§16.2(v) Behavior with Respect to Parameters

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3: 8.21 Generalized Sine and Cosine Integrals

§8.21 Generalized Sine and Cosine Integrals

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§8.21(i) Definitions: General Values

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§8.21(iv) Interrelations

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§8.21(v) Special Values

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4: 1.16 Distributions

… ► $\mathrm{\Lambda }:𝒟(I)\to ℂ$ is called a distribution, or generalized function, if it is a continuous linear functional on $𝒟(I)$, that is, it is a linear functional and for every ${\varphi }_n\to \varphi$ in $𝒟(I)$, … ►More generally, for $\alpha :[a,b]\to [-\mathrm{\infty },\mathrm{\infty }]$ a nondecreasing function the corresponding Lebesgue–Stieltjes measure ${\mu }_{\alpha }$ (see §1.4(v)) can be considered as a distribution: … ►More generally, if $\alpha (x)$ is an infinitely differentiable function, then … ►Friedman (1990) gives an overview of generalized functions and their relation to distributions. …

5: 35.8 Generalized Hypergeometric Functions of Matrix Argument

§35.8 Generalized Hypergeometric Functions of Matrix Argument

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§35.8(i) Definition

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Convergence Properties

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§35.8(iv) General Properties

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Confluence

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6: 25.10 Zeros

… ►More than 41% of all the zeros in the critical strip lie on the critical line (Bui et al. (2011)). …

7: 19.2 Definitions

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§19.2(i) General Elliptic Integrals

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8: Bibliography B

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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.

Encodings:

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

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External Links:

Document, ZentralBlatt

Referenced by:

§16.6.

Encodings:

BibTeX

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Generalized Hypergeometric Series. Stechert-Hafner, Inc., New York.

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External Links:

MathReview

Referenced by:

§16.4(iii), §16.4(iii), §16.4(iii), §16.4(iii), §16.4(iii), §17.1, §17.4(i), Ch.17.

Encodings:

BibTeX

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Zeros of generalized Airy functions. Mathematika 32 (1), pp. 104–117.

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External Links:

ISSN 0025-5793, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§9.13(ii).

Encodings:

BibTeX

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More than 41% of the zeros of the zeta function are on the critical line. Acta Arith. 150 (1), pp. 35–64.

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External Links:

ISSN 0065-1036, Document, Link, MathReview (Timothy S. Trudgian), ZentralBlatt

Referenced by:

§25.10(ii), §25.10(ii), Erratum (V1.1.4) for Subsection 25.10(ii).

Encodings:

BibTeX

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9: Publications

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Using Numerical Grid Generation to Facilitate 3D Visualization of Complicated Mathematical Functions, Technical Report NISTIR 6413 (November 1999), National Institute of Standards and Technology.

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From 2D to 3D: Numerical Grid Generation and the Visualization of Complex Surfaces, Proceedings of the 7th International Conference on Numerical Grid Generation in Computational Field Simulations, Whistler, British Columbia, Canada, September 25-28, 2000.

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Boundary/Contour Fitted Grid Generation for Effective Visualizations in a Digital Library of Mathematical Functions, Proceedings of the 9th International Conference on Numerical Grid Generation in Computational Field Simulations, San Jose, June 11–18, 2005. pp. 61–71.

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Web-Based 3D Visualization in a Digital Library of Mathematical Functions, Proceedings of the Web3D Symposium, Bangor, UK, March 29–April 1, 2005.

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Methods of Relevance Ranking and Hit-content Generation in Math Search, Proceedings of Mathematical Knowledge Management (MKM2007), RISC, Hagenberg, Austria, June 27–30, 2007.

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10: Peter L. Walker

… ►Walker is now retired and living in Cheltenham, UK. …