DLMF:23.21.E2 (Q7382): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12104 / rank
 
Normal rank
Property / Symbols used: Q12104 / qualifier
 
Defining formula:

ζ 𝜁 {\displaystyle{\displaystyle\zeta}}

\zeta
Property / Symbols used: Q12104 / qualifier
 
xml-id: C23.S21.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q12105 / rank
 
Normal rank
Property / Symbols used: Q12105 / qualifier
 
Defining formula:

f ⁢ ( ρ ) 𝑓 𝜌 {\displaystyle{\displaystyle f(\rho)}}

f(\rho)
Property / Symbols used: Q12105 / qualifier
 
xml-id: C23.S21.XMD5.m1dec

Latest revision as of 01:22, 2 January 2020

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DLMF:23.21.E2
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    Statements

    Defining formula
    ( η - ζ ) ⁢ ( ζ - ξ ) ⁢ ( ξ - η ) ⁢ ∇ 2 = ( ζ - η ) ⁢ f ⁢ ( ξ ) ⁢ f ′ ⁢ ( ξ ) ⁢ ∂ ∂ ⁡ ξ + ( ξ - ζ ) ⁢ f ⁢ ( η ) ⁢ f ′ ⁢ ( η ) ⁢ ∂ ∂ ⁡ η + ( η - ξ ) ⁢ f ⁢ ( ζ ) ⁢ f ′ ⁢ ( ζ ) ⁢ ∂ ∂ ⁡ ζ , 𝜂 𝜁 𝜁 𝜉 𝜉 𝜂 superscript ∇ 2 𝜁 𝜂 𝑓 𝜉 superscript 𝑓 ′ 𝜉 partial-derivative 𝜉 𝜉 𝜁 𝑓 𝜂 superscript 𝑓 ′ 𝜂 partial-derivative 𝜂 𝜂 𝜉 𝑓 𝜁 superscript 𝑓 ′ 𝜁 partial-derivative 𝜁 {\displaystyle{\displaystyle(\eta-\zeta)(\zeta-\xi)(\xi-\eta)\nabla^{2}=(\zeta% -\eta)f(\xi)f^{\prime}(\xi)\frac{\partial}{\partial\xi}+(\xi-\zeta)f(\eta)f^{% \prime}(\eta)\frac{\partial}{\partial\eta}+(\eta-\xi)f(\zeta)f^{\prime}(\zeta)% \frac{\partial}{\partial\zeta},}}
    0 references
    DLMF id
    DLMF:23.21.E2
    0 references
    Symbols used
    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    ∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
    xml-id
    C1.S5.E3.m4adec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2adec
    0 references
    Q12102
    Defining formula
    ξ 𝜉 {\displaystyle{\displaystyle\xi}}
    xml-id
    C23.S21.XMD1.m1dec
    0 references
    Q12103
    Defining formula
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C23.S21.XMD2.m1dec
    0 references
    Q12104
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C23.S21.XMD3.m1dec
    0 references
    Q12105
    Defining formula
    f ⁢ ( ρ ) 𝑓 𝜌 {\displaystyle{\displaystyle f(\rho)}}
    xml-id
    C23.S21.XMD5.m1dec
    0 references
     
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