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1: 27.17 Other Applications

… ►Schroeder (2006) describes many of these applications, including the design of concert hall ceilings to scatter sound into broad lateral patterns for improved acoustic quality, precise measurements of delays of radar echoes from Venus and Mercury to confirm one of the relativistic effects predicted by Einstein’s theory of general relativity, and the use of primes in creating artistic graphical designs.

2: About Color Map

… ►The conventional CMYK color wheel (not to be confused with the traditional Artist’s color wheel) places the additive colors (red, green, blue) and the subtractive colors (yellow, cyan, magenta) at multiples of 60 degrees. …

3: 25.10 Zeros

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

4: Browsers

… ►Although we have attempted to follow standards and maintain backwards compatibility with older browsers, you will generally get the best results by upgrading to the latest version of your preferred browser.

5: Bibliography B

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Numerical evaluation of the zero-order Hankel transform using Filon quadrature philosophy. Appl. Math. Lett. 9 (5), pp. 21–26.

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External Links:

ISSN 0893-9659, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

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Irregular primes to one million. Math. Comp. 59 (200), pp. 717–722.

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External Links:

ISSN 0025-5718, FullText, MathReview (Duncan A. Buell), ZentralBlatt

Referenced by:

2nd item.

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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6: 21.1 Special Notation

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$g,h$	positive integers.
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$a\circ b$	intersection index of $a$ and $b$, two cycles lying on a closed surface. $a\circ b=0$ if $a$ and $b$ do not intersect. Otherwise $a\circ b$ gets an additive contribution from every intersection point. This contribution is $1$ if the basis of the tangent vectors of the $a$ and $b$ cycles (§21.7(i)) at the point of intersection is positively oriented; otherwise it is $-1$.
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7: Guide to Searching the DLMF

… ►Be careful, however, because if you put quotes around math expressions involving math symbols, you may not get the matches you’d expect. …

8: 4.10 Integrals

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9: 13 Confluent Hypergeometric Functions

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10: 19.22 Quadratic Transformations

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19.22.5 $$2p_{\pm }=\sqrt{(p+x)(p+y)}\pm \sqrt{(p-x)(p-y)},$$

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Defines:

$p_{\pm }$: modified parameter (locally)

Referenced by:

§19.22(iii), §19.22(iii)

Permalink:

http://dlmf.nist.gov/19.22.E5

Encodings:

pMML, png, TeX

See also:

Annotations for §19.22(i), §19.22 and Ch.19

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$4(p_{\pm }^2-a^2)={(\sqrt{p^2-x^2}\pm \sqrt{p^2-y^2})}^2.$

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$2z_{\pm }=\sqrt{(z+x)(z+y)}\pm \sqrt{(z-x)(z-y)},$

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$4(z_{\pm }^2-a^2)={(\sqrt{z^2-x^2}\pm \sqrt{z^2-y^2})}^2.$

… ►However, if $x$ and $y$ are complex conjugates and $z$ and $p$ are real, then the right-hand sides of all transformations in §§19.22(i) and 19.22(iii)—except (19.22.3) and (19.22.22)—are free of complex numbers and $p_{\pm }^2-p_{\mp }^2=\pm |p^2-x^2|\ne 0$. …