DLMF:4.39.E1 (Q1970): Difference between revisions

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Property / constraint
 

z ± 1 2 π i , ± 3 2 π i , 𝑧 plus-or-minus 1 2 𝜋 imaginary-unit plus-or-minus 3 2 𝜋 imaginary-unit {\displaystyle{\displaystyle z\neq\pm\tfrac{1}{2}\pi\mathrm{i},\pm\tfrac{3}{2}% \pi\mathrm{i},\dots}}

z\neq\pm\tfrac{1}{2}\pi\iunit,\pm\tfrac{3}{2}\pi\iunit,\dots
Property / constraint: z ± 1 2 π i , ± 3 2 π i , 𝑧 plus-or-minus 1 2 𝜋 imaginary-unit plus-or-minus 3 2 𝜋 imaginary-unit {\displaystyle{\displaystyle z\neq\pm\tfrac{1}{2}\pi\mathrm{i},\pm\tfrac{3}{2}% \pi\mathrm{i},\dots}} / rank
 
Normal rank

Revision as of 16:03, 30 December 2019

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DLMF:4.39.E1
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    Statements

    tanh z = z 1 + z 2 3 + z 2 5 + z 2 7 + , 𝑧 continued-fraction 𝑧 1 continued-fraction superscript 𝑧 2 3 continued-fraction superscript 𝑧 2 5 continued-fraction superscript 𝑧 2 7 {\displaystyle{\displaystyle\tanh z=\cfrac{z}{1+\cfrac{z^{2}}{3+\cfrac{z^{2}}{% 5+\cfrac{z^{2}}{7+\cdots}}}},}}
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    z ± 1 2 π i , ± 3 2 π i , 𝑧 plus-or-minus 1 2 𝜋 imaginary-unit plus-or-minus 3 2 𝜋 imaginary-unit {\displaystyle{\displaystyle z\neq\pm\tfrac{1}{2}\pi\mathrm{i},\pm\tfrac{3}{2}% \pi\mathrm{i},\dots}}
    0 references