general properties

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1: 35.8 Generalized Hypergeometric Functions of Matrix Argument

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Convergence Properties

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§35.8(iv) General Properties

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2: 16.2 Definition and Analytic Properties

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§16.2(ii) Case $p\leq q$

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§16.2(iii) Case $p=q+1$

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§16.2(iv) Case $p>q+1$

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§16.2(v) Behavior with Respect to Parameters

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3: 16.5 Integral Representations and Integrals

… ►where the contour of integration separates the poles of

\Gamma\left(a_{k}+s\right)

k=1,\dots,p

, from those of

\Gamma\left(-s\right)

. …

4: Bibliography R

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J. Raynal (1979) On the definition and properties of generalized

6

j

symbols. J. Math. Phys. 20 (12), pp. 2398–2415.

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External Links:: ISSN 0022-2488, Document, MathReview (S. Saran), ZentralBlatt
Referenced by:: §16.4(iii), §16.4(iii).
Encodings:: BibTeX

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D. St. P. Richards (2004) Total positivity properties of generalized hypergeometric functions of matrix argument. J. Statist. Phys. 116 (1-4), pp. 907–922.

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External Links:: ISSN 0022-4715, Document, MathReview (Stamatis Koumandos), ZentralBlatt
Referenced by:: §35.9.
Encodings:: BibTeX

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5: Bibliography B

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V. Britanak, P. C. Yip, and K. R. Rao (2007) Discrete Cosine and Sine Transforms. General Properties, Fast Algorithms and Integer Approximations. Elsevier/Academic Press, Amsterdam.

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External Links:: ISBN 978-0-12-373624-6; 0-12-373624-2, MathReview (Gerd Teschke)
Referenced by:: §18.3.
Encodings:: BibTeX

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6: 1.15 Summability Methods

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General Cesàro Summability

… ►and satisfies the property …

7: 25.16 Mathematical Applications

… ►For further properties of

H\left(s,z\right)

see Apostol and Vu (1984). …

8: Bibliography C

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P. A. Clarkson and K. Jordaan (2018) Properties of generalized Freud polynomials. J. Approx. Theory 225, pp. 148–175.

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External Links:: ISSN 0021-9045, Document, Link, MathReview (Maria das Neves Rebocho)
Referenced by:: §18.32.
Encodings:: BibTeX

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9: 9.13 Generalized Airy Functions

… ►Properties of

A_{n}\left(z\right)

and

B_{n}\left(z\right)

follow from the corresponding properties of the modified Bessel functions. … ►The distribution in

\mathbb{C}

and asymptotic properties of the zeros of

A_{n}\left(z\right)

A_{n}'\left(z\right)

B_{n}\left(z\right)

, and

B_{n}'\left(z\right)

are investigated in Swanson and Headley (1967) and Headley and Barwell (1975). …

10: 18.5 Explicit Representations

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18.5.5

p_{n}(x)=\frac{1}{\kappa_{n}w(x)}\frac{{\mathrm{d}}^{n}}{{\mathrm{d}x}^{n}}% \left(w(x)(F(x))^{n}\right).

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Symbols:: $\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}$ : derivative of $f$ with respect to $x$ , $p_{n}(x)$ : polynomial of degree $n$ , $w(x)$ : weight function, $n$ : nonnegative integer and $x$ : real variable
A&S Ref:: 22.1.6 (incorrectly stated as property of general OP’s)
Referenced by:: §18.17(v), §18.17(vi), §18.17(vii), item 3., §18.39(ii), §18.39(ii), Table 18.5.1, §18.9(iii)
Permalink:: http://dlmf.nist.gov/18.5.E5
Encodings:: pMML, png, TeX
See also:: Annotations for §18.5(ii), §18.5 and Ch.18

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