DLMF:4.19.E4 (Q1683): Difference between revisions

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Property / constraint
 

0 < | z | < π 0 𝑧 𝜋 {\displaystyle{\displaystyle 0<|z|<\pi}}

0<|z|<\pi
Property / constraint: 0 < | z | < π 0 𝑧 𝜋 {\displaystyle{\displaystyle 0<|z|<\pi}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q11109 / rank
 
Normal rank
Property / Symbols used: Q11109 / qualifier
 
test:

B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}

\BernoullinumberB{\NVar{n}}
Property / Symbols used: Q11109 / qualifier
 
xml-id: C24.S2.SS1.m1aadec
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.m2aadec
Property / Symbols used
 
Property / Symbols used: cosecant function / rank
 
Normal rank
Property / Symbols used: cosecant function / qualifier
 
test:

csc ⁡ z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}

\csc@@{\NVar{z}}
Property / Symbols used: cosecant function / qualifier
 
xml-id: C4.S14.E5.m2adec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5acdec
Property / Symbols used
 
Property / Symbols used: Q11223 / rank
 
Normal rank
Property / Symbols used: Q11223 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11223 / qualifier
 
xml-id: C4.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1cdec

Latest revision as of 17:21, 1 January 2020

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DLMF:4.19.E4
No description defined

    Statements

    test
    csc ⁡ z = 1 z + z 6 + 7 360 ⁢ z 3 + 31 15120 ⁢ z 5 + ⋯ + ( - 1 ) n - 1 ⁢ 2 ⁢ ( 2 2 ⁢ n - 1 - 1 ) ⁢ B 2 ⁢ n ( 2 ⁢ n ) ! ⁢ z 2 ⁢ n - 1 + ⋯ , 𝑧 1 𝑧 𝑧 6 7 360 superscript 𝑧 3 31 15120 superscript 𝑧 5 ⋯ superscript 1 𝑛 1 2 superscript 2 2 𝑛 1 1 Bernoulli-number-B 2 𝑛 2 𝑛 superscript 𝑧 2 𝑛 1 ⋯ {\displaystyle{\displaystyle\csc z=\frac{1}{z}+\frac{z}{6}+\frac{7}{360}z^{3}+% \frac{31}{15120}z^{5}+\cdots+\frac{(-1)^{n-1}2(2^{2n-1}-1)B_{2n}}{(2n)!}z^{2n-% 1}+\cdots,}}
    0 references
    DLMF id
    DLMF:4.19.E4
    0 references
    constraint
    0 < | z | < π 0 𝑧 𝜋 {\displaystyle{\displaystyle 0<|z|<\pi}}
    0 references
    Symbols used
    Q11109
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    cosecant function
    test
    csc ⁡ z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}
    xml-id
    C4.S14.E5.m2adec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    Q11223
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1adec
    0 references
    Q11217
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1cdec
    0 references
     
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