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11: Bibliography Q

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On two problems concerning means. J. Hangzhou Inst. Elec. Engrg. 17, pp. 1–7 (Chinese).

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Notes:

In Chinese

Referenced by:

§19.9(i).

Encodings:

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12: Staff

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George E. Andrews, Pennsylvania State University, Chap. 17

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George E. Andrews, Pennsylvania State University, for Chap. 17

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13: 4.22 Infinite Products and Partial Fractions

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14: Notices

… ►Pursuant to Title 17 USC 105, the National Institute of Standards and Technology (NIST), United States Department of Commerce, is authorized to receive and hold copyrights transferred to it by assignment or otherwise. …

15: 26.2 Basic Definitions

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Table 26.2.1: Partitions $p\left(n\right)$.

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$n$	$p\left(n\right)$	$n$	$p\left(n\right)$	$n$	$p\left(n\right)$
0	1	17	297	34	12310
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16: 26.6 Other Lattice Path Numbers

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Table 26.6.1: Delannoy numbers $D(m,n)$.

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$m$	$n$
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1	1	3	5	7	9	11	13	15	17	19	21
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8	1	17	145	833	3649	13073	40081	1 08545	2 65729	5 98417	12 56465
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Table 26.6.2: Motzkin numbers $M(n)$.

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$n$	$M(n)$	$n$	$M(n)$	$n$	$M(n)$	$n$	$M(n)$	$n$	$M(n)$
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1	1	5	21	9	835	13	41835	17	23 56779
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Table 26.6.4: Schröder numbers $r(n)$.

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$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$
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$1$	$2$	$5$	$394$	$9$	$\mathrm{2\hspace{0.33em}06098}$	$13$	$\mathrm{1420\hspace{0.33em}78746}$	$17$	$\mathrm{11\hspace{0.33em}18180\hspace{0.33em}26018}$
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17: 1.11 Zeros of Polynomials

… ►Resolvent cubic is $z^3+12z^2+20z+9=0$ with roots ${\theta }_1=-1$, ${\theta }_2=-\frac{1}{2}(11+\sqrt{85})$, ${\theta }_3=-\frac{1}{2}(11-\sqrt{85})$, and $\sqrt{-{\theta }_1}=1$, $\sqrt{-{\theta }_2}=\frac{1}{2}(\sqrt{17}+\sqrt{5})$, $\sqrt{-{\theta }_3}=\frac{1}{2}(\sqrt{17}-\sqrt{5})$. So $2{\alpha }_1=1+\sqrt{17}$, $2{\alpha }_2=1-\sqrt{17}$, $2{\alpha }_3=-1+\sqrt{5}$, $2{\alpha }_4=-1-\sqrt{5}$, and the roots of $f(z)=0$ are $\frac{1}{2}(3\pm \sqrt{17})$, $\frac{1}{2}(1\pm \sqrt{5})$. …

18: Bibliography I

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Asymptotics of the Askey-Wilson and $q$-Jacobi polynomials. SIAM J. Math. Anal. 17 (6), pp. 1475–1482.

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External Links:

ISSN 0036-1410, Document, MathReview (David M. Bressoud), ZentralBlatt

Referenced by:

§18.29.

Encodings:

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Connection formulae for the fourth Painlevé transcendent; Clarkson-McLeod solution. J. Phys. A 31 (17), pp. 4073–4113.

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External Links:

ISSN 0305-4470, Document, MathReview (Yoshitsugu Takei), ZentralBlatt

Referenced by:

§32.11(v).

Encodings:

BibTeX

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19: Bibliography Z

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Mathieu functions for purely imaginary parameters. J. Comput. Appl. Math. 236 (17), pp. 4513–4524.

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External Links:

ISSN 0377-0427, Document, FullText, MathReview (Bartolomeu D. B. Figueiredo), ZentralBlatt

Referenced by:

§28.36(iii), §28.36(iii).

Encodings:

BibTeX

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Fast evaluation of elementary mathematical functions with correctly rounded last bit. ACM Trans. Math. Software 17 (3), pp. 410–423.

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External Links:

ISSN 0098-3500, Document, ZentralBlatt

Referenced by:

§4.45(i).

Encodings:

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20: 23.18 Modular Transformations

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