DLMF:4.24.E5 (Q1799): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1aadec

Revision as of 18:38, 1 January 2020

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DLMF:4.24.E5
No description defined

    Statements

    Defining formula
    arctan ⁡ z = z z 2 + 1 ⁢ ( 1 + 2 3 ⁢ z 2 1 + z 2 + 2 ⋅ 4 3 ⋅ 5 ⁢ ( z 2 1 + z 2 ) 2 + ⋯ ) , 𝑧 𝑧 superscript 𝑧 2 1 1 2 3 superscript 𝑧 2 1 superscript 𝑧 2 ⋅ 2 4 ⋅ 3 5 superscript superscript 𝑧 2 1 superscript 𝑧 2 2 ⋯ {\displaystyle{\displaystyle\operatorname{arctan}z=\frac{z}{z^{2}+1}\*\left(1+% \frac{2}{3}\frac{z^{2}}{1+z^{2}}+\frac{2\cdot 4}{3\cdot 5}\left(\frac{z^{2}}{1% +z^{2}}\right)^{2}+\cdots\right),}}
    0 references
    DLMF id
    DLMF:4.24.E5
    0 references
    constraint
    ℜ ⁡ ( z 2 ) > - 1 2 superscript 𝑧 2 1 2 {\displaystyle{\displaystyle\Re(z^{2})>-\tfrac{1}{2}}}
    0 references
    Symbols used
    Q10816
    Defining formula
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7abdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
    0 references
     
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