DLMF:20.2.E2 (Q6742): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(5 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11946 / rank
 
Normal rank
Property / Symbols used: Q11946 / qualifier
 
Defining formula:

θ j ⁡ ( z | τ ) Jacobi-theta-tau 𝑗 𝑧 𝜏 {\displaystyle{\displaystyle\theta_{\NVar{j}}\left(\NVar{z}\middle|\NVar{\tau}% \right)}}

\Jacobithetatau{\NVar{j}}@{\NVar{z}}{\NVar{\tau}}
Property / Symbols used: Q11946 / qualifier
 
xml-id: C20.S2.SS1.m1aadec
Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2adec
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.m1adec
Property / Symbols used
 
Property / Symbols used: Q11948 / rank
 
Normal rank
Property / Symbols used: Q11948 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11948 / qualifier
 
xml-id: C20.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11949 / rank
 
Normal rank
Property / Symbols used: Q11949 / qualifier
 
Defining formula:

τ 𝜏 {\displaystyle{\displaystyle\tau}}

\tau
Property / Symbols used: Q11949 / qualifier
 
xml-id: C20.S1.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q11950 / rank
 
Normal rank
Property / Symbols used: Q11950 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11950 / qualifier
 
xml-id: C20.S1.XMD5.m1adec

Latest revision as of 14:28, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:20.2.E2
No description defined

    Statements

    Defining formula
    θ 2 ⁡ ( z | τ ) = θ 2 ⁡ ( z , q ) = 2 ⁢ ∑ n = 0 ∞ q ( n + 1 2 ) 2 ⁢ cos ⁡ ( ( 2 ⁢ n + 1 ) ⁢ z ) , Jacobi-theta-tau 2 𝑧 𝜏 Jacobi-theta 2 𝑧 𝑞 2 superscript subscript 𝑛 0 superscript 𝑞 superscript 𝑛 1 2 2 2 𝑛 1 𝑧 {\displaystyle{\displaystyle\theta_{2}\left(z\middle|\tau\right)=\theta_{2}% \left(z,q\right)=2\sum\limits_{n=0}^{\infty}q^{(n+\frac{1}{2})^{2}}\cos\left((% 2n+1)z\right),}}
    0 references
    DLMF id
    DLMF:20.2.E2
    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.m2aadec
    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.m1aadec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    Q11947
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C20.S1.XMD2.m1adec
    0 references
    Q11948
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C20.S1.XMD3.m1adec
    0 references
    Q11949
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C20.S1.XMD4.m1adec
    0 references
    Q11950
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C20.S1.XMD5.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6742&oldid=47423"