DLMF:19.5.E8 (Q6137): 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: Q11820 / rank
 
Normal rank
Property / Symbols used: Q11820 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11820 / qualifier
 
xml-id: C19.S1.XMD3.m1adec

Revision as of 13:40, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:19.5.E8
No description defined

    Statements

    Defining formula
    K ⁡ ( k ) = π 2 ⁢ ( 1 + 2 ⁢ ∑ n = 1 ∞ q n 2 ) 2 , complete-elliptic-integral-first-kind-K 𝑘 𝜋 2 superscript 1 2 superscript subscript 𝑛 1 superscript 𝑞 superscript 𝑛 2 2 {\displaystyle{\displaystyle K\left(k\right)=\frac{\pi}{2}\left(1+2\sum_{n=1}^% {\infty}q^{n^{2}}\right)^{2},}}
    0 references
    DLMF id
    DLMF:19.5.E8
    0 references
    constraint
    | q | < 1 𝑞 1 {\displaystyle{\displaystyle|q|<1}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1abdec
    0 references
    nome
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C22.S2.E1.m2abdec
    0 references
    Q11820
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C19.S1.XMD3.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6137&oldid=38791"