DLMF:4.40.E8 (Q1980): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1agdec
Property / Symbols used
 
Property / Symbols used: hyperbolic sine function / rank
 
Normal rank
Property / Symbols used: hyperbolic sine function / qualifier
 
test:

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

\sinh@@{\NVar{z}}
Property / Symbols used: hyperbolic sine function / qualifier
 
xml-id: C4.S28.E1.m2addec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3agdec
Property / Symbols used
 
Property / Symbols used: tangent function / rank
 
Normal rank
Property / Symbols used: tangent function / qualifier
 
test:

tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}

\tan@@{\NVar{z}}
Property / Symbols used: tangent function / qualifier
 
xml-id: C4.S14.E4.m2adec
Property / Symbols used
 
Property / Symbols used: Q11221 / rank
 
Normal rank
Property / Symbols used: Q11221 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11221 / qualifier
 
xml-id: C4.S1.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q11218 / rank
 
Normal rank
Property / Symbols used: Q11218 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11218 / qualifier
 
xml-id: C4.S1.XMD6.m1gdec

Latest revision as of 18:22, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:4.40.E8
No description defined

    Statements

    test
    ∫ 0 ∞ sinh ⁡ ( a ⁢ x ) sinh ⁡ ( π ⁢ x ) ⁢ d x = 1 2 ⁢ tan ⁡ ( 1 2 ⁢ a ) , superscript subscript 0 𝑎 𝑥 𝜋 𝑥 𝑥 1 2 1 2 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{\sinh\left(ax\right)}{\sinh% \left(\pi x\right)}\mathrm{d}x=\tfrac{1}{2}\tan\left(\tfrac{1}{2}a\right),}}
    0 references
    DLMF id
    DLMF:4.40.E8
    0 references
    constraint
    - π < a < π 𝜋 𝑎 𝜋 {\displaystyle{\displaystyle-\pi<a<\pi}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
    0 references
    hyperbolic sine function
    test
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2addec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
    0 references
    tangent function
    test
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2adec
    0 references
    Q11221
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1adec
    0 references
    Q11218
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1gdec
    0 references
     
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