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11—20 of 49 matching pages

11: Guide to Searching the DLMF

… ►From there you can also access an advanced search page where you can control certain settings, narrowing the search to certain chapters, or restricting the results to equations, graphs, tables, or bibliographic items. …

12: 21.3 Symmetry and Quasi-Periodicity

… ►Because of this property, the elements of $𝜶$ and $𝜷$ are usually restricted to $[0,1)$, without loss of generality. …

13: 8.2 Definitions and Basic Properties

… ►without restrictions on the integration paths. … ►without restriction on $a$. …

14: 16.5 Integral Representations and Integrals

… ►In (16.5.3) the restriction can be removed when . …Lastly, the restrictions on the parameters can be eased by replacing the integration paths with loop contours; see Luke (1969a, §3.6). …

15: 8.21 Generalized Sine and Cosine Integrals

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16: 10.23 Sums

… ►If $𝒞=J$ and the upper signs are taken, then the restriction on $\lambda$ is unnecessary. … ►The restriction is unnecessary when $𝒞=J$ and $\nu$ is an integer. … ►The restriction is unnecessary in (10.23.7) when $𝒞=J$ and $\nu$ is an integer, and in (10.23.8) when $𝒞=J$. …

17: 4.8 Identities

… ►The restriction on $z_1$ can be removed when $z_2$ is an integer.

18: 4.24 Inverse Trigonometric Functions: Further Properties

… ►

4.24.2 $$\arccos z={(2(1-z))}^{1/2}\left(1+\sum _{n=1}^{\mathrm{\infty }}\frac{1\cdot 3\cdot 5\mathrm{\cdots }(2n-1)}{2^{2n}(2n+1)n!}{(1-z)}^n\right),$$ $|1-z|\le 2$.

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Symbols:

$!$: factorial (as in $n!$), $\arccos z$: arccosine function, $n$: integer and $z$: complex variable

A&S Ref:

4.4.41 (which is stated differently and the constraint on $z$ is more restrictive.)

Permalink:

http://dlmf.nist.gov/4.24.E2

Encodings:

pMML, png, TeX

See also:

Annotations for §4.24(i), §4.24 and Ch.4

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19: Mathematical Introduction

… ►This is because $𝐅$ is akin to the notation used for Bessel functions (§10.2(ii)), inasmuch as $𝐅$ is an entire function of each of its parameters $a$, $b$, and $c$:​ this results in fewer restrictions and simpler equations. …

20: 11.6 Asymptotic Expansions

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