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1: 7.20 Mathematical Applications

… ►Furthermore, because $dy/dx=\tan \left(\frac{1}{2}\pi t^2\right)$, the angle between the $x$-axis and the tangent to the spiral at $P(t)$ is given by $\frac{1}{2}\pi t^2$. …

2: 1.9 Calculus of a Complex Variable

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Conformal Transformation

… ►The angle between $C_1$ and $C_2$ at $z_0$ is the angle between the tangents to the two arcs at $z_0$, that is, the difference of the signed angles that the tangents make with the positive direction of the real axis. If $f^{\prime }(z_0)\ne 0$, then the angle between $C_1$ and $C_2$ equals the angle between $C_1^{\prime }$ and $C_2^{\prime }$ both in magnitude and sense. …

3: 1.6 Vectors and Vector-Valued Functions

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1.6.4 $$\cos \theta =\frac{𝐚\cdot 𝐛}{\Vert 𝐚\Vert \Vert 𝐛\Vert };$$

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Symbols:

$\cos z$: cosine function, $\Vert 𝐯\Vert$: vector norm ($l$²) and $\theta$: angle between $𝐚$ and $𝐛$

Permalink:

http://dlmf.nist.gov/1.6.E4

Encodings:

pMML, png, TeX

See also:

Annotations for §1.6(i), §1.6(i), §1.6 and Ch.1

► $\theta$ is the angle between $𝐚$ and $𝐛$. … ►

1.6.9

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Symbols:

$det$: determinant, $\sin z$: sine function, $\Vert 𝐯\Vert$: vector norm ($l$²), $\theta$: angle between $𝐚$ and $𝐛$ , $𝐢$: unit vector, $𝐣$: unit vector and $𝐤$: unit vector

Referenced by:

§1.6(i)

Permalink:

http://dlmf.nist.gov/1.6.E9

Encodings:

pMML, png, TeX

See also:

Annotations for §1.6(i), §1.6(i), §1.6 and Ch.1

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4: 3.2 Linear Algebra

… ►Because $\left|{𝐲}^{\mathrm{T}}𝐱\right|=\left|\cos \theta \right|$, where $\theta$ is the angle between ${𝐲}^{\mathrm{T}}$ and $𝐱$ we always have $\kappa (\lambda )\ge 1$. …

5: 31.16 Mathematical Applications

… ►Expansions of Heun polynomial products in terms of Jacobi polynomial (§18.3) products are derived in Kalnins and Miller (1991a, b, 1993) from the viewpoint of interrelation between two bases in a Hilbert space: ►

31.16.1 $${\mathrm{𝐻𝑝}}_{n,m}\left(x\right){\mathrm{𝐻𝑝}}_{n,m}\left(y\right)=\sum _{j=0}^n{A}_j{\sin }^{2j}\theta P_{n-j}^{(\gamma +\delta +2j-1,ϵ-1)}\left(\cos \left(2\theta \right)\right)P_j^{(\delta -1,\gamma -1)}\left(\cos \left(2\varphi \right)\right),$$

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Symbols:

${\mathrm{𝐻𝑝}}_{n,m}(a,q_{n,m};-n,\beta ,\gamma ,\delta ;z)$: Heun polynomials, $P_n^{(\alpha ,\beta )}\left(x\right)$: Jacobi polynomial, $\cos z$: cosine function, $\sin z$: sine function, $\gamma$: real or complex parameter, $\delta$: real or complex parameter, $ϵ$: real or complex parameter, $j$: nonnegative integer, $m$: nonnegative integer, $n$: nonnegative integer, $a$: complex parameter, $q$: real or complex parameter, $\beta$: real or complex parameter, $\theta$: angle, $\varphi$: angle, $x$: variable, $y$: variable and $A_j$: coefficients

Referenced by:

§31.16(ii), §31.16(ii)

Permalink:

http://dlmf.nist.gov/31.16.E1

Encodings:

pMML, png, TeX

See also:

Annotations for §31.16(ii), §31.16 and Ch.31

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6: 2.1 Definitions and Elementary Properties

… ►means that for each $n$, the difference between $f(x)$ and the $n$th partial sum on the right-hand side is $O\left({(x-c)}^n\right)$ as $x\to c$ in $𝐗$. … ►For (2.1.14) $𝐗$ can be the positive real axis or any unbounded sector in $ℂ$ of finite angle. …