DLMF:2.10.E21 (Q1008): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: cotangent function / rank
 
Normal rank
Property / Symbols used: cotangent function / qualifier
 
Defining formula:

cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}

\cot@@{\NVar{z}}
Property / Symbols used: cotangent function / qualifier
 
xml-id: C4.S14.E7.m2aadec

Revision as of 17:35, 1 January 2020

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DLMF:2.10.E21
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    Statements

    Defining formula
    cot ⁡ ( π ⁢ t ) 2 ⁢ i = - 1 2 - 1 e - 2 ⁢ π ⁢ i ⁢ t - 1 = 1 2 + 1 e 2 ⁢ π ⁢ i ⁢ t - 1 , 𝜋 𝑡 2 𝑖 1 2 1 superscript 𝑒 2 𝜋 𝑖 𝑡 1 1 2 1 superscript 𝑒 2 𝜋 𝑖 𝑡 1 {\displaystyle{\displaystyle\frac{\cot\left(\pi t\right)}{2i}=-\frac{1}{2}-% \frac{1}{e^{-2\pi it}-1}=\frac{1}{2}+\frac{1}{e^{2\pi it}-1},}}
    0 references
    DLMF id
    DLMF:2.10.E21
    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.m2acdec
    0 references
    cotangent function
    Defining formula
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2aadec
    0 references
     
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