DLMF:2.3.E29 (Q749): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10950 / rank
 
Normal rank
Property / Symbols used: Q10950 / qualifier
 
Defining formula:

λ 𝜆 {\displaystyle{\displaystyle\lambda}}

\lambda
Property / Symbols used: Q10950 / qualifier
 
xml-id: C2.S3.XMD8.m1ldec

Latest revision as of 16:55, 1 January 2020

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DLMF:2.3.E29
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    Statements

    Defining formula
    I ⁢ ( α , x ) = e - x ⁢ p ⁢ ( α , 0 ) ⁢ ∫ 0 κ exp ⁡ ( - x ⁢ ( 1 2 ⁢ w 2 - a ⁢ w ) ) ⁢ f ⁢ ( α , w ) ⁢ w λ - 1 ⁢ d w , 𝐼 𝛼 𝑥 superscript 𝑒 𝑥 𝑝 𝛼 0 superscript subscript 0 𝜅 𝑥 1 2 superscript 𝑤 2 𝑎 𝑤 𝑓 𝛼 𝑤 superscript 𝑤 𝜆 1 𝑤 {\displaystyle{\displaystyle I(\alpha,x)=e^{-xp(\alpha,0)}\*\int_{0}^{\kappa}% \exp\left(-x\left(\tfrac{1}{2}w^{2}-aw\right)\right)f(\alpha,w)w^{\lambda-1}% \mathrm{d}w,}}
    0 references
    DLMF id
    DLMF:2.3.E29
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aodec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2addec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2amdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aodec
    0 references
    integral (locally)
    Defining formula
    I ⁢ ( α , x ) 𝐼 𝛼 𝑥 {\displaystyle{\displaystyle I(\alpha,x)}}
    xml-id
    C2.S3.XMD27.m1adec
    0 references
    Q10964
    Defining formula
    p ⁢ ( α , t ) 𝑝 𝛼 𝑡 {\displaystyle{\displaystyle p(\alpha,t)}}
    xml-id
    C2.S3.XMD28.m1edec
    0 references
    Q10966
    Defining formula
    w 𝑤 {\displaystyle{\displaystyle w}}
    xml-id
    C2.S3.XMD30.m1cdec
    0 references
    Q10967
    Defining formula
    a ⁢ ( α ) 𝑎 𝛼 {\displaystyle{\displaystyle a(\alpha)}}
    xml-id
    C2.S3.XMD31.m1bdec
    0 references
    function (locally)
    Defining formula
    f ⁢ ( α , w ) 𝑓 𝛼 𝑤 {\displaystyle{\displaystyle f(\alpha,w)}}
    xml-id
    C2.S3.XMD33.m1dec
    0 references
    Q10969
    Defining formula
    κ = w ⁢ ( k ) 𝜅 𝑤 𝑘 {\displaystyle{\displaystyle\kappa=w(k)}}
    xml-id
    C2.S3.XMD34.m1dec
    0 references
    Q10950
    Defining formula
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C2.S3.XMD8.m1ldec
    0 references
     
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