DLMF:4.25.E3 (Q1814): 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.m1bdec

Latest revision as of 18:39, 1 January 2020

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DLMF:4.25.E3
No description defined

    Statements

    Defining formula
    arcsin ⁡ z 1 - z 2 = z 1 - 1 ⋅ 2 ⁢ z 2 3 - 1 ⋅ 2 ⁢ z 2 5 - 3 ⋅ 4 ⁢ z 2 7 - 3 ⋅ 4 ⁢ z 2 9 - ⁢ ⋯ , 𝑧 1 superscript 𝑧 2 continued-fraction 𝑧 1 continued-fraction ⋅ 1 2 superscript 𝑧 2 3 continued-fraction ⋅ 1 2 superscript 𝑧 2 5 continued-fraction ⋅ 3 4 superscript 𝑧 2 7 continued-fraction ⋅ 3 4 superscript 𝑧 2 limit-from 9 ⋯ {\displaystyle{\displaystyle\frac{\operatorname{arcsin}z}{\sqrt{1-z^{2}}}=% \cfrac{z}{1-\cfrac{1\cdot 2z^{2}}{3-\cfrac{1\cdot 2z^{2}}{5-\cfrac{3\cdot 4z^{% 2}}{7-\cfrac{3\cdot 4z^{2}}{9-}}}}}\cdots,}}
    0 references
    DLMF id
    DLMF:4.25.E3
    0 references
    Symbols used
    Q11242
    Defining formula
    arcsin ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m5adec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1bdec
    0 references
     
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