DLMF:4.36.E2 (Q1916): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: hyperbolic cosine function / rank
 
Normal rank
Property / Symbols used: hyperbolic cosine function / qualifier
 
Defining formula:

cosh z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}

\cosh@@{\NVar{z}}
Property / Symbols used: hyperbolic cosine function / qualifier
 
xml-id: C4.S28.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q11223 / rank
 
Normal rank
Property / Symbols used: Q11223 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11223 / qualifier
 
xml-id: C4.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1adec

Latest revision as of 19:13, 1 January 2020

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DLMF:4.36.E2
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    Statements

    cosh z = n = 1 ( 1 + 4 z 2 ( 2 n - 1 ) 2 π 2 ) . 𝑧 superscript subscript product 𝑛 1 1 4 superscript 𝑧 2 superscript 2 𝑛 1 2 superscript 𝜋 2 {\displaystyle{\displaystyle\cosh z=\prod_{n=1}^{\infty}\left(1+\frac{4z^{2}}{% (2n-1)^{2}\pi^{2}}\right).}}
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    DLMF:4.36.E2
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    cosh z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    C4.S28.E2.m2adec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C4.S1.XMD3.m1adec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1adec
    0 references