DLMF:20.2.E1 (Q6741): 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: Q11947 / rank
 
Normal rank
Property / Symbols used: Q11947 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11947 / qualifier
 
xml-id: C20.S1.XMD2.m1dec

Revision as of 14:27, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:20.2.E1
No description defined

    Statements

    Defining formula
    θ 1 ⁡ ( z | τ ) = θ 1 ⁡ ( z , q ) = 2 ⁢ ∑ n = 0 ∞ ( - 1 ) n ⁢ q ( n + 1 2 ) 2 ⁢ sin ⁡ ( ( 2 ⁢ n + 1 ) ⁢ z ) , Jacobi-theta-tau 1 𝑧 𝜏 Jacobi-theta 1 𝑧 𝑞 2 superscript subscript 𝑛 0 superscript 1 𝑛 superscript 𝑞 superscript 𝑛 1 2 2 2 𝑛 1 𝑧 {\displaystyle{\displaystyle\theta_{1}\left(z\middle|\tau\right)=\theta_{1}% \left(z,q\right)=2\sum\limits_{n=0}^{\infty}(-1)^{n}q^{(n+\frac{1}{2})^{2}}% \sin\left((2n+1)z\right),}}
    0 references
    DLMF id
    DLMF:20.2.E1
    0 references
    Symbols used
    Q11945
    Defining formula
    θ j ⁡ ( z , q ) Jacobi-theta 𝑗 𝑧 𝑞 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z},\NVar{q}\right)}}
    xml-id
    C20.S2.SS1.m2adec
    0 references
    Q11946
    Defining formula
    θ j ⁡ ( z | τ ) Jacobi-theta-tau 𝑗 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}% \right)}}
    xml-id
    C20.S2.SS1.m1adec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6741&oldid=47366"