DLMF:4.19.E3 (Q1682): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5abdec

Revision as of 18:21, 1 January 2020

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DLMF:4.19.E3
No description defined

    Statements

    Defining formula
    tan ⁡ z = z + z 3 3 + 2 15 ⁢ z 5 + 17 315 ⁢ z 7 + ⋯ + ( - 1 ) n - 1 ⁢ 2 2 ⁢ n ⁢ ( 2 2 ⁢ n - 1 ) ⁢ B 2 ⁢ n ( 2 ⁢ n ) ! ⁢ z 2 ⁢ n - 1 + ⋯ , 𝑧 𝑧 superscript 𝑧 3 3 2 15 superscript 𝑧 5 17 315 superscript 𝑧 7 ⋯ superscript 1 𝑛 1 superscript 2 2 𝑛 superscript 2 2 𝑛 1 Bernoulli-number-B 2 𝑛 2 𝑛 superscript 𝑧 2 𝑛 1 ⋯ {\displaystyle{\displaystyle\tan z=z+\frac{z^{3}}{3}+\frac{2}{15}z^{5}+\frac{1% 7}{315}z^{7}+\cdots+\frac{(-1)^{n-1}2^{2n}(2^{2n}-1)B_{2n}}{(2n)!}z^{2n-1}+% \cdots,}}
    0 references
    DLMF id
    DLMF:4.19.E3
    0 references
    constraint
    | z | < 1 2 ⁢ π 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|z|<\frac{1}{2}\pi}}
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
     
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