DLMF:10.13.E8 (Q3133): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11428 / qualifier
 
xml-id: C10.S1.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1gdec

Latest revision as of 15:22, 2 January 2020

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DLMF:10.13.E8
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    Statements

    Defining formula
    w ( 2 ⁢ n ) = ( - 1 ) n ⁢ λ 2 ⁢ n ⁢ z - n ⁢ w , superscript 𝑤 2 𝑛 superscript 1 𝑛 superscript 𝜆 2 𝑛 superscript 𝑧 𝑛 𝑤 {\displaystyle{\displaystyle w^{(2n)}=(-1)^{n}\lambda^{2n}z^{-n}w,}}
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    DLMF id
    DLMF:10.13.E8
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    comment
    Warning: Falling back to standard tex;
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    constraint
    w = z 1 2 ⁢ n ⁢ 𝒞 n ⁡ ( 2 ⁢ λ ⁢ e k ⁢ π ⁢ i / n ⁢ z 1 2 ) 𝑤 superscript 𝑧 1 2 𝑛 cylinder-function 𝑛 2 𝜆 superscript 𝑒 𝑘 𝜋 imaginary-unit 𝑛 superscript 𝑧 1 2 {\displaystyle{\displaystyle w=z^{\frac{1}{2}n}\mathscr{C}_{n}\left(2\lambda e% ^{k\pi\mathrm{i}/n}z^{\frac{1}{2}}\right)}}
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    w = z 1 2 ⁢ n 𝒞 n ( 2 λ e k ⁢ π ⁢ i / n z 1 missing fragments w superscript 𝑧 1 2 𝑛 subscript 𝒞 𝑛 fragments ( 2 λ superscript 𝑒 𝑘 𝜋 i 𝑛 superscript 𝑧 1 missing {\displaystyle{\displaystyle w=z^{\frac{1}{2}n}\mathscr{C}_{n}\left(2\lambda e% ^{k\pi\mathrm{i}/n}z^{\frac{1}{missing}\)\@add@PDF@RDFa@triples\end{document}}}}
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    k = 0 , 1 , … , 2 ⁢ n - 1 𝑘 0 1 … 2 𝑛 1 {\displaystyle{\displaystyle k=0,1,\ldots,2n-1}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q11430
    Defining formula
    𝒞 ν ⁡ ( z ) cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.Px5.p1.m3agdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1dec
    0 references
    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1dec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1gdec
    0 references
     
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