DLMF:14.12.E9 (Q4830): Difference between revisions

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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.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11593 / rank
 
Normal rank
Property / Symbols used: Q11593 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11593 / qualifier
 
xml-id: C14.S1.XMD5.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11602 / rank
 
Normal rank
Property / Symbols used: Q11602 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11602 / qualifier
 
xml-id: C14.S1.XMD6.m1adec
Property / Symbols used
 
Property / Symbols used: Q11606 / rank
 
Normal rank
Property / Symbols used: Q11606 / qualifier
 
test:

u 𝑢 {\displaystyle{\displaystyle u}}

u
Property / Symbols used: Q11606 / qualifier
 
xml-id: C14.S12.XMD1.m1dec

Latest revision as of 00:44, 2 January 2020

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English
DLMF:14.12.E9
No description defined

    Statements

    test
    𝑸 n m ⁡ ( x ) = 1 n ! ⁢ ∫ 0 u ( x - ( x 2 - 1 ) 1 / 2 ⁢ cosh ⁡ t ) n ⁢ cosh ⁡ ( m ⁢ t ) ⁢ d t , associated-Legendre-black-Q 𝑚 𝑛 𝑥 1 𝑛 superscript subscript 0 𝑢 superscript 𝑥 superscript superscript 𝑥 2 1 1 2 𝑡 𝑛 𝑚 𝑡 𝑡 {\displaystyle{\displaystyle\boldsymbol{Q}^{m}_{n}\left(x\right)=\frac{1}{n!}% \int_{0}^{u}\left(x-\left(x^{2}-1\right)^{1/2}\cosh t\right)^{n}\cosh\left(mt% \right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:14.12.E9
    0 references
    Symbols used
    Q11592
    test
    𝑸 ν μ ⁡ ( z ) associated-Legendre-black-Q 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(% \NVar{z}\right)}}
    xml-id
    C14.S21.SS1.p1.m3aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    hyperbolic cosine function
    test
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2acdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
    0 references
    Q11589
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1fdec
    0 references
    Q11593
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C14.S1.XMD5.m1bdec
    0 references
    Q11602
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C14.S1.XMD6.m1adec
    0 references
    Q11606
    test
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C14.S12.XMD1.m1dec
    0 references
     
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