DLMF:4.9.E1 (Q1609): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2adec

Revision as of 17:13, 1 January 2020

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DLMF:4.9.E1
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    Statements

    test
    ln ⁡ ( 1 + z ) = z 1 + z 2 + z 3 + 4 ⁢ z 4 + 4 ⁢ z 5 + 9 ⁢ z 6 + 9 ⁢ z 7 + ⁢ ⋯ , 1 𝑧 continued-fraction 𝑧 1 continued-fraction 𝑧 2 continued-fraction 𝑧 3 continued-fraction 4 𝑧 4 continued-fraction 4 𝑧 5 continued-fraction 9 𝑧 6 continued-fraction 9 𝑧 limit-from 7 ⋯ {\displaystyle{\displaystyle\ln\left(1+z\right)=\cfrac{z}{1+\cfrac{z}{2+\cfrac% {z}{3+\cfrac{4z}{4+\cfrac{4z}{5+\cfrac{9z}{6+\cfrac{9z}{7+}}}}}}}\cdots,}}
    0 references
    DLMF id
    DLMF:4.9.E1
    0 references
    constraint
    | ph ⁡ ( 1 + z ) | < π phase 1 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(1+z\right)|<\pi}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
     
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