DLMF:4.19.E7 (Q1686): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(6 intermediate revisions by the same user not shown)
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.m1acdec
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.m2addec
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.m5afdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2aadec
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.m1ddec
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.m1fdec

Latest revision as of 17:22, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:4.19.E7
No description defined

    Statements

    test
    ln ⁡ ( sin ⁡ z z ) = ∑ n = 1 ∞ ( - 1 ) n ⁢ 2 2 ⁢ n - 1 ⁢ B 2 ⁢ n n ⁢ ( 2 ⁢ n ) ! ⁢ z 2 ⁢ n , 𝑧 𝑧 superscript subscript 𝑛 1 superscript 1 𝑛 superscript 2 2 𝑛 1 Bernoulli-number-B 2 𝑛 𝑛 2 𝑛 superscript 𝑧 2 𝑛 {\displaystyle{\displaystyle\ln\left(\frac{\sin z}{z}\right)=\sum_{n=1}^{% \infty}\frac{(-1)^{n}2^{2n-1}B_{2n}}{n(2n)!}z^{2n},}}
    0 references
    DLMF id
    DLMF:4.19.E7
    0 references
    constraint
    | z | < π 𝑧 𝜋 {\displaystyle{\displaystyle|z|<\pi}}
    0 references
    Symbols used
    Q11109
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5afdec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    Q11223
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1ddec
    0 references
    Q11217
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1fdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q1686&oldid=7910"