DLMF:5.12.E7 (Q2152): Difference between revisions

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Property / constraint
 

a > | b | 𝑎 𝑏 {\displaystyle{\displaystyle\Re a>|\Re b|}}

\realpart@@{a}>|\realpart@@{b}|
Property / constraint: a > | b | 𝑎 𝑏 {\displaystyle{\displaystyle\Re a>|\Re b|}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: beta function / rank
 
Normal rank
Property / Symbols used: beta function / qualifier
 
test:

B ( a , b ) Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}

\EulerBeta@{\NVar{a}}{\NVar{b}}
Property / Symbols used: beta function / qualifier
 
xml-id: C5.S12.E1.m2afdec
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.m1afdec
Property / Symbols used
 
Property / Symbols used: hyperbolic cosine function / rank
 
Normal rank
Property / Symbols used: hyperbolic cosine function / qualifier
 
test:

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: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3afdec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1abdec
Property / Symbols used
 
Property / Symbols used: Q11275 / rank
 
Normal rank
Property / Symbols used: Q11275 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11275 / qualifier
 
xml-id: C5.S1.XMD8.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11283 / rank
 
Normal rank
Property / Symbols used: Q11283 / qualifier
 
test:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q11283 / qualifier
 
xml-id: C5.S1.XMD9.m1fdec

Latest revision as of 18:44, 1 January 2020

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DLMF:5.12.E7
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    Statements

    0 cosh ( 2 b t ) ( cosh t ) 2 a d t = 4 a - 1 B ( a + b , a - b ) , superscript subscript 0 2 𝑏 𝑡 superscript 𝑡 2 𝑎 𝑡 superscript 4 𝑎 1 Euler-Beta 𝑎 𝑏 𝑎 𝑏 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{\cosh\left(2bt\right)}{(% \cosh t)^{2a}}\mathrm{d}t=4^{a-1}\mathrm{B}\left(a+b,a-b\right),}}
    0 references
    0 references
    a > | b | 𝑎 𝑏 {\displaystyle{\displaystyle\Re a>|\Re b|}}
    0 references
    B ( a , b ) Euler-Beta 𝑎 𝑏 {\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}
    C5.S12.E1.m2afdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1afdec
    0 references
    cosh z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    C4.S28.E2.m2adec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3afdec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1abdec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C5.S1.XMD8.m1fdec
    0 references
    b 𝑏 {\displaystyle{\displaystyle b}}
    C5.S1.XMD9.m1fdec
    0 references