DLMF:4.25.E5 (Q1816): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1ddec

Latest revision as of 18:39, 1 January 2020

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DLMF:4.25.E5
No description defined

    Statements

    Defining formula
    e 2 ⁢ a ⁢ arctan ⁡ ( 1 / z ) = 1 + 2 ⁢ a z - a + a 2 + 1 3 ⁢ z + a 2 + 4 5 ⁢ z + a 2 + 9 7 ⁢ z + ⁢ ⋯ , superscript 𝑒 2 𝑎 1 𝑧 1 continued-fraction 2 𝑎 𝑧 𝑎 continued-fraction superscript 𝑎 2 1 3 𝑧 continued-fraction superscript 𝑎 2 4 5 𝑧 continued-fraction superscript 𝑎 2 9 limit-from 7 𝑧 ⋯ {\displaystyle{\displaystyle e^{2a\operatorname{arctan}\left(1/z\right)}={1+% \cfrac{2a}{z-a+\cfrac{a^{2}+1}{3z+\cfrac{a^{2}+4}{5z+\cfrac{a^{2}+9}{7z+}}}}% \cdots,}}}
    0 references
    DLMF id
    DLMF:4.25.E5
    0 references
    Symbols used
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10816
    Defining formula
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7aadec
    0 references
    Q11221
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1adec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1ddec
    0 references
     
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