DLMF:4.36.E1 (Q1915): 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.m2adec
Property / Symbols used
 
Property / Symbols used: hyperbolic sine function / rank
 
Normal rank
Property / Symbols used: hyperbolic sine function / qualifier
 
Defining formula:

sinh z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}

\sinh@@{\NVar{z}}
Property / Symbols used: hyperbolic sine function / qualifier
 
xml-id: C4.S28.E1.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.m1dec
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.m1dec

Latest revision as of 19:13, 1 January 2020

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DLMF:4.36.E1
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    Statements

    sinh z = z n = 1 ( 1 + z 2 n 2 π 2 ) , 𝑧 𝑧 superscript subscript product 𝑛 1 1 superscript 𝑧 2 superscript 𝑛 2 superscript 𝜋 2 {\displaystyle{\displaystyle\sinh z=z\prod_{n=1}^{\infty}\left(1+\frac{z^{2}}{% n^{2}\pi^{2}}\right),}}
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    DLMF:4.36.E1
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    sinh z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    C4.S28.E1.m2adec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C4.S1.XMD3.m1dec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1dec
    0 references