DLMF:1.15.E20 (Q562): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Abel mean (locally) / rank
 
Normal rank
Property / Symbols used: Abel mean (locally) / qualifier
 
Defining formula:

A ⁢ ( r , θ ) 𝐴 𝑟 𝜃 {\displaystyle{\displaystyle A(r,\theta)}}

A(r,\theta)
Property / Symbols used: Abel mean (locally) / qualifier
 
xml-id: C1.S15.XMD3.m1adec

Latest revision as of 16:29, 1 January 2020

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English
DLMF:1.15.E20
No description defined

    Statements

    Defining formula
    A ⁢ ( r , θ ) = 1 2 ⁢ π ⁢ ∫ 0 2 ⁢ π P ⁢ ( r , θ - t ) ⁢ f ⁢ ( t ) ⁢ d t . 𝐴 𝑟 𝜃 1 2 𝜋 subscript superscript 2 𝜋 0 𝑃 𝑟 𝜃 𝑡 𝑓 𝑡 𝑡 {\displaystyle{\displaystyle A(r,\theta)=\frac{1}{2\pi}\int^{2\pi}_{0}P(r,% \theta-t)f(t)\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:1.15.E20
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Poisson kernel (locally)
    Defining formula
    P ⁢ ( r , θ ) 𝑃 𝑟 𝜃 {\displaystyle{\displaystyle P(r,\theta)}}
    xml-id
    C1.S15.XMD1.m1cdec
    0 references
    Abel mean (locally)
    Defining formula
    A ⁢ ( r , θ ) 𝐴 𝑟 𝜃 {\displaystyle{\displaystyle A(r,\theta)}}
    xml-id
    C1.S15.XMD3.m1adec
    0 references
     
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