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

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Property / 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)}}

w=z^{\frac{1}{2}n}\BesselC{n}@{2\lambda e^{k\pi\iunit/n}z^{\frac{1}{2}}}
Property / 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)}} / rank
 
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Revision as of 17:16, 30 December 2019

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DLMF:10.13.E8
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    Statements

    test
    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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