DLMF:14.17.E13 (Q4894): 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.m1aldec
Property / Symbols used
 
Property / Symbols used: psi (or digamma) function / rank
 
Normal rank
Property / Symbols used: psi (or digamma) function / qualifier
 
test:

ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}

\digamma@{\NVar{z}}
Property / Symbols used: psi (or digamma) function / qualifier
 
xml-id: C5.S2.E2.m2acdec
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.m3aldec
Property / Symbols used
 
Property / Symbols used: Q11596 / rank
 
Normal rank
Property / Symbols used: Q11596 / qualifier
 
test:

𝖰 ν ⁡ ( x ) = 𝖰 ν 0 ⁡ ( x ) shorthand-Ferrers-Legendre-Q-first-kind 𝜈 𝑥 Ferrers-Legendre-Q-first-kind 0 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{Q}^{0}_{\nu}\left(x\right)}}

\FerrersQ[]{\NVar{\nu}}@{\NVar{x}}=\FerrersQ[0]{\nu}@{x}
Property / Symbols used: Q11596 / qualifier
 
xml-id: C14.S2.SS2.p2.m4aadec
Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1ldec

Latest revision as of 12:24, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:14.17.E13
No description defined

    Statements

    test
    ∫ - 1 1 ( 𝖰 ν ⁡ ( x ) ) 2 ⁢ d x = π 2 - 2 ⁢ ( 1 + cos 2 ⁡ ( ν ⁢ π ) ) ⁢ ψ ′ ⁡ ( ν + 1 ) 2 ⁢ ( 2 ⁢ ν + 1 ) , superscript subscript 1 1 superscript shorthand-Ferrers-Legendre-Q-first-kind 𝜈 𝑥 2 𝑥 superscript 𝜋 2 2 1 2 𝜈 𝜋 diffop digamma 1 𝜈 1 2 2 𝜈 1 {\displaystyle{\displaystyle\int_{-1}^{1}\left(\mathsf{Q}_{\nu}\left(x\right)% \right)^{2}\mathrm{d}x=\frac{\pi^{2}-2\left(1+{\cos^{2}}\left(\nu\pi\right)% \right)\psi'\left(\nu+1\right)}{2(2\nu+1)},}}
    0 references
    DLMF id
    DLMF:14.17.E13
    0 references
    constraint
    - 1 , - 2 , - 3 , … 1 2 3 … {\displaystyle{\displaystyle-1,-2,-3,\dots}}
    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.m2acdec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
    0 references
    psi (or digamma) function
    test
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2acdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aldec
    0 references
    Q11596
    test
    𝖰 ν ⁡ ( x ) = 𝖰 ν 0 ⁡ ( x ) shorthand-Ferrers-Legendre-Q-first-kind 𝜈 𝑥 Ferrers-Legendre-Q-first-kind 0 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{Q}^{0}_{\nu}\left(x\right)}}
    xml-id
    C14.S2.SS2.p2.m4aadec
    0 references
    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1ldec
    0 references
     
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