DLMF:30.11.E6 (Q8901): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: order not exceeding / rank
 
Normal rank
Property / Symbols used: order not exceeding / qualifier
 
Defining formula:

O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

\bigO@{\NVar{x}}
Property / Symbols used: order not exceeding / qualifier
 
xml-id: C2.S1.E3.m2adec

Revision as of 01:48, 2 January 2020

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DLMF:30.11.E6
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    S n m ( j ) ( z , γ ) = { ψ n ( j ) ( γ z ) + O ( z - 2 e | z | ) , j = 1 , 2 , ψ n ( j ) ( γ z ) ( 1 + O ( z - 1 ) ) , j = 3 , 4 . radial-spheroidal-wave-S 𝑚 𝑗 𝑛 𝑧 𝛾 cases superscript subscript 𝜓 𝑛 𝑗 𝛾 𝑧 Big-O superscript 𝑧 2 superscript 𝑒 𝑧 𝑗 1 2 superscript subscript 𝜓 𝑛 𝑗 𝛾 𝑧 1 Big-O superscript 𝑧 1 𝑗 3 4 {\displaystyle{\displaystyle S^{m(j)}_{n}\left(z,\gamma\right)=\begin{cases}% \psi_{n}^{(j)}(\gamma z)+O\left(z^{-2}e^{|\Im z|}\right),&j=1,2,\\ \psi_{n}^{(j)}(\gamma z)\left(1+O\left(z^{-1}\right)\right),&j=3,4.\end{cases}}}
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    DLMF:30.11.E6
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    O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2adec
    0 references