DLMF:4.25.E2 (Q1813): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / constraint
 

a z ± 1 2 π , ± 3 2 π , 𝑎 𝑧 plus-or-minus 1 2 𝜋 plus-or-minus 3 2 𝜋 {\displaystyle{\displaystyle az\neq\pm\tfrac{1}{2}\pi,\pm\tfrac{3}{2}\pi,\dots}}

az\neq\pm\tfrac{1}{2}\pi,\pm\tfrac{3}{2}\pi,\dots
Property / constraint: a z ± 1 2 π , ± 3 2 π , 𝑎 𝑧 plus-or-minus 1 2 𝜋 plus-or-minus 3 2 𝜋 {\displaystyle{\displaystyle az\neq\pm\tfrac{1}{2}\pi,\pm\tfrac{3}{2}\pi,\dots}} / rank
 
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Revision as of 17:02, 30 December 2019

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DLMF:4.25.E2
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    Statements

    tan ( a z ) = a tan z 1 + ( 1 - a 2 ) tan 2 z 3 + ( 4 - a 2 ) tan 2 z 5 + ( 9 - a 2 ) tan 2 z 7 + , 𝑎 𝑧 continued-fraction 𝑎 𝑧 1 continued-fraction 1 superscript 𝑎 2 2 𝑧 3 continued-fraction 4 superscript 𝑎 2 2 𝑧 5 continued-fraction 9 superscript 𝑎 2 2 𝑧 limit-from 7 {\displaystyle{\displaystyle\tan\left(az\right)=\cfrac{a\tan z}{1+\cfrac{(1-a^% {2}){\tan^{2}}z}{3+\cfrac{(4-a^{2}){\tan^{2}}z}{5+\cfrac{(9-a^{2}){\tan^{2}}z}% {7+}}}}\cdots,}}
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    DLMF:4.25.E2
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    | z | < 1 2 π 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\Re z|<\tfrac{1}{2}\pi}}
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    | z | < 1 2 π 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\Re z|<\tfrac{1}{2}\pi}}
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    a z ± 1 2 π , ± 3 2 π , 𝑎 𝑧 plus-or-minus 1 2 𝜋 plus-or-minus 3 2 𝜋 {\displaystyle{\displaystyle az\neq\pm\tfrac{1}{2}\pi,\pm\tfrac{3}{2}\pi,\dots}}
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