DLMF:11.10.E36 (Q4058): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Anger function / rank
 
Normal rank
Property / Symbols used: Anger function / qualifier
 
Defining formula:

𝐉 ν ( z ) Anger-J 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{J}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\AngerJ{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Anger function / qualifier
 
xml-id: C11.S10.E1.m2asdec

Revision as of 14:59, 2 January 2020

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DLMF:11.10.E36
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    Statements

    z 𝐉 ν ( z ) ± ν 𝐉 ν ( z ) = ± z 𝐉 ν 1 ( z ) ± sin ( π ν ) π , plus-or-minus 𝑧 diffop Anger-J 𝜈 1 𝑧 𝜈 Anger-J 𝜈 𝑧 plus-or-minus plus-or-minus 𝑧 Anger-J minus-or-plus 𝜈 1 𝑧 𝜋 𝜈 𝜋 {\displaystyle{\displaystyle z\mathbf{J}_{\nu}'\left(z\right)\pm\nu\mathbf{J}_% {\nu}\left(z\right)=\pm z\mathbf{J}_{\nu\mp 1}\left(z\right)\pm\frac{\sin\left% (\pi\nu\right)}{\pi},}}
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    DLMF:11.10.E36
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    𝐉 ν ( z ) Anger-J 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{J}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C11.S10.E1.m2asdec
    0 references