DLMF:19.12.E2 (Q6299): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11818 / rank
 
Normal rank
Property / Symbols used: Q11818 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11818 / qualifier
 
xml-id: C19.S1.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11808 / rank
 
Normal rank
Property / Symbols used: Q11808 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11808 / qualifier
 
xml-id: C19.S1.XMD5.m1adec
Property / Symbols used
 
Property / Symbols used: Q11815 / rank
 
Normal rank
Property / Symbols used: Q11815 / qualifier
 
test:

k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}

k^{\prime}
Property / Symbols used: Q11815 / qualifier
 
xml-id: C19.S1.XMD6.m1adec
Property / Symbols used
 
Property / Symbols used: Q11851 / rank
 
Normal rank
Property / Symbols used: Q11851 / qualifier
 
test:

d ⁢ ( m ) 𝑑 𝑚 {\displaystyle{\displaystyle d(m)}}

d(m)
Property / Symbols used: Q11851 / qualifier
 
xml-id: C19.S12.XMD1.m1adec

Latest revision as of 12:49, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:19.12.E2
No description defined

    Statements

    test
    E ⁡ ( k ) = 1 + 1 2 ⁢ ∑ m = 0 ∞ ( 1 2 ) m ⁢ ( 3 2 ) m ( 2 ) m ⁢ m ! ⁢ k ′ 2 ⁢ m + 2 ⁢ ( ln ⁡ ( 1 k ′ ) + d ⁢ ( m ) - 1 ( 2 ⁢ m + 1 ) ⁢ ( 2 ⁢ m + 2 ) ) , complete-elliptic-integral-second-kind-E 𝑘 1 1 2 superscript subscript 𝑚 0 Pochhammer 1 2 𝑚 Pochhammer 3 2 𝑚 Pochhammer 2 𝑚 𝑚 superscript superscript 𝑘 ′ 2 𝑚 2 1 superscript 𝑘 ′ 𝑑 𝑚 1 2 𝑚 1 2 𝑚 2 {\displaystyle{\displaystyle E\left(k\right)=1+\frac{1}{2}\sum_{m=0}^{\infty}% \frac{{\left(\tfrac{1}{2}\right)_{m}}{\left(\tfrac{3}{2}\right)_{m}}}{{\left(2% \right)_{m}}m!}{k^{\prime}}^{2m+2}\*\left(\ln\left(\frac{1}{k^{\prime}}\right)% +d(m)-\frac{1}{(2m+1)(2m+2)}\right),}}
    0 references
    DLMF id
    DLMF:19.12.E2
    0 references
    constraint
    | k ′ | < 1 superscript 𝑘 ′ 1 {\displaystyle{\displaystyle|k^{\prime}|<1}}
    0 references
    Symbols used
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    Q11601
    test
    E ⁡ ( k ) complete-elliptic-integral-second-kind-E 𝑘 {\displaystyle{\displaystyle E\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m2adec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q11818
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C19.S1.XMD2.m1adec
    0 references
    Q11808
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1adec
    0 references
    Q11815
    test
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C19.S1.XMD6.m1adec
    0 references
    Q11851
    test
    d ⁢ ( m ) 𝑑 𝑚 {\displaystyle{\displaystyle d(m)}}
    xml-id
    C19.S12.XMD1.m1adec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q6299&oldid=35834"