DLMF:17.8.E3 (Q5422): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11718 / rank
 
Normal rank
Property / Symbols used: Q11718 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11718 / qualifier
 
xml-id: C17.S1.XMD7.m1bdec

Latest revision as of 15:05, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:17.8.E3
No description defined

    Statements

    Defining formula
    ∑ n = - ∞ ∞ ( - 1 ) n ⁢ q n ⁢ ( 3 ⁢ n - 1 ) / 2 ⁢ z 3 ⁢ n ⁢ ( 1 + z ⁢ q n ) = ( q , - z , - q / z ; q ) ∞ ⁢ ( q ⁢ z 2 , q / z 2 ; q 2 ) ∞ . superscript subscript 𝑛 superscript 1 𝑛 superscript 𝑞 𝑛 3 𝑛 1 2 superscript 𝑧 3 𝑛 1 𝑧 superscript 𝑞 𝑛 q-multiple-Pochhammer 𝑞 𝑧 𝑞 𝑧 𝑞 q-multiple-Pochhammer 𝑞 superscript 𝑧 2 𝑞 superscript 𝑧 2 superscript 𝑞 2 {\displaystyle{\displaystyle\sum_{n=-\infty}^{\infty}(-1)^{n}q^{n(3n-1)/2}z^{3% n}(1+zq^{n})=\left(q,-z,-q/z;q\right)_{\infty}\left(qz^{2},q/{z^{2}};q^{2}% \right)_{\infty}.}}
    0 references
    DLMF id
    DLMF:17.8.E3
    0 references
    Symbols used
    Q11713
    Defining formula
    ( a 1 , a 2 , … , a r ; q ) n q-multiple-Pochhammer subscript 𝑎 1 subscript 𝑎 2 … subscript 𝑎 𝑟 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m6abdec
    0 references
    Q11710
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1bdec
    0 references
    Q11711
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1adec
    0 references
    Q11718
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C17.S1.XMD7.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5422&oldid=54044"