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

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎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.m5aadec

Revision as of 13:49, 2 January 2020

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

    Statements

    Defining formula
    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
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    Q11601
    Defining formula
    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
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6299&oldid=40513"