DLMF:25.10.E3 (Q7673): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q12151 / rank
 
Normal rank
Property / Symbols used: Q12151 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12151 / qualifier
 
xml-id: C25.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q12148 / rank
 
Normal rank
Property / Symbols used: Q12148 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12148 / qualifier
 
xml-id: C25.S1.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q12158 / rank
 
Normal rank
Property / Symbols used: Q12158 / qualifier
 
Defining formula:

Z ( t ) 𝑍 𝑡 {\displaystyle{\displaystyle Z(t)}}

Z(t)
Property / Symbols used: Q12158 / qualifier
 
xml-id: C25.S10.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q12159 / rank
 
Normal rank
Property / Symbols used: Q12159 / qualifier
 
Defining formula:

ϑ ( t ) italic-ϑ 𝑡 {\displaystyle{\displaystyle\vartheta(t)}}

\vartheta(t)
Property / Symbols used: Q12159 / qualifier
 
xml-id: C25.S10.XMD2.m1bdec

Latest revision as of 13:35, 2 January 2020

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English
DLMF:25.10.E3
No description defined

    Statements

    Z ( t ) = 2 n = 1 m cos ( ϑ ( t ) - t ln n ) n 1 / 2 + R ( t ) , 𝑍 𝑡 2 superscript subscript 𝑛 1 𝑚 italic-ϑ 𝑡 𝑡 𝑛 superscript 𝑛 1 2 𝑅 𝑡 {\displaystyle{\displaystyle Z(t)=2\sum_{n=1}^{m}\frac{\cos\left(\vartheta(t)-% t\ln n\right)}{n^{1/2}}+R(t),}}
    0 references
    DLMF:25.10.E3
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aadec
    0 references
    m 𝑚 {\displaystyle{\displaystyle m}}
    C25.S1.XMD2.m1dec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C25.S1.XMD3.m1dec
    0 references
    Z ( t ) 𝑍 𝑡 {\displaystyle{\displaystyle Z(t)}}
    C25.S10.XMD1.m1adec
    0 references
    ϑ ( t ) italic-ϑ 𝑡 {\displaystyle{\displaystyle\vartheta(t)}}
    C25.S10.XMD2.m1bdec
    0 references