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21—30 of 107 matching pages
21: 27.2 Functions
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►An equivalent form states that the th prime (when the primes are listed in increasing order) is asymptotic to as :
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27.2.8
►and if is the smallest positive integer such that , then is a primitive root mod .
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22: Guide to Searching the DLMF
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►To recognize the math symbols and structures, and to accommodate equivalence between various notations and various forms of expression, the search system maps the math part of your queries into a different form.
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23: 12.4 Power-Series Expansions
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►Equivalently,
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24: 24.19 Methods of Computation
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►For number-theoretic applications it is important to compute for ; in particular to find the irregular pairs
for which .
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25: 25.13 Periodic Zeta Function
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25.13.3
if ; if .
26: 26.9 Integer Partitions: Restricted Number and Part Size
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►The conjugate partition is obtained by reflecting the Ferrers graph across the main diagonal or, equivalently, by representing each integer by a column of dots.
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►equivalently, partitions into at most parts either have exactly parts, in which case we can subtract one from each part, or they have strictly fewer than parts.
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27: 34.4 Definition: Symbol
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►Except in degenerate cases the combination of the triangle inequalities for the four symbols in (34.4.1) is equivalent to the existence of a tetrahedron (possibly degenerate) with edges of lengths ; see Figure 34.4.1.
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►Equivalently,
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28: 10.72 Mathematical Applications
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►In regions in which (10.72.1) has a simple turning point , that is, and are analytic (or with weaker conditions if is a real variable) and is a simple zero of , asymptotic expansions of the solutions for large can be constructed in terms of Airy functions or equivalently Bessel functions or modified Bessel functions of order (§9.6(i)).
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