DLMF:28.32.E4 (Q8553): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
 
Defining formula:

∂ ⁡ f ∂ ⁡ x partial-derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}

\pderiv{\NVar{f}}{\NVar{x}}
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S5.E3.m4abdec
Property / Symbols used
 
Property / Symbols used: partial differential of $$x$$ / rank
 
Normal rank
Property / Symbols used: partial differential of $$x$$ / qualifier
 
Defining formula:

∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}

\pdiff{\NVar{x}}
Property / Symbols used: partial differential of $$x$$ / qualifier
 
xml-id: C1.S5.E3.m2abdec
Property / Symbols used
 
Property / Symbols used: Q12271 / rank
 
Normal rank
Property / Symbols used: Q12271 / qualifier
 
Defining formula:

q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}

q=h^{2}
Property / Symbols used: Q12271 / qualifier
 
xml-id: C28.S1.XMD10.m1dec
Property / Symbols used
 
Property / Symbols used: Q12272 / rank
 
Normal rank
Property / Symbols used: Q12272 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12272 / qualifier
 
xml-id: C28.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q12335 / rank
 
Normal rank
Property / Symbols used: Q12335 / qualifier
 
Defining formula:

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

\zeta
Property / Symbols used: Q12335 / qualifier
 
xml-id: C28.S32.XMD5.m1dec
Property / Symbols used
 
Property / Symbols used: Q12336 / rank
 
Normal rank
Property / Symbols used: Q12336 / qualifier
 
Defining formula:

K ⁢ ( z , ζ ) 𝐾 𝑧 𝜁 {\displaystyle{\displaystyle K(z,\zeta)}}

K(z,\zeta)
Property / Symbols used: Q12336 / qualifier
 
xml-id: C28.S32.XMD7.m1dec

Latest revision as of 15:40, 2 January 2020

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DLMF:28.32.E4
No description defined

    Statements

    Defining formula
    ∂ 2 ⁡ K ∂ ⁡ z 2 - ∂ 2 ⁡ K ∂ ⁡ ζ 2 = 2 ⁢ q ⁢ ( cos ⁡ ( 2 ⁢ z ) - cos ⁡ ( 2 ⁢ ζ ) ) ⁢ K . partial-derivative 𝐾 𝑧 2 partial-derivative 𝐾 𝜁 2 2 𝑞 2 𝑧 2 𝜁 𝐾 {\displaystyle{\displaystyle\frac{{\partial}^{2}K}{{\partial z}^{2}}-\frac{{% \partial}^{2}K}{{\partial\zeta}^{2}}=2q\left(\cos\left(2z\right)-\cos\left(2% \zeta\right)\right)K.}}
    0 references
    DLMF id
    DLMF:28.32.E4
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
    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.m4abdec
    0 references
    partial differential of $$x$$
    Defining formula
    ∂ ⁡ x 𝑥 {\displaystyle{\displaystyle\partial\NVar{x}}}
    xml-id
    C1.S5.E3.m2abdec
    0 references
    Q12271
    Defining formula
    q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}}
    xml-id
    C28.S1.XMD10.m1dec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1dec
    0 references
    Q12335
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C28.S32.XMD5.m1dec
    0 references
    Q12336
    Defining formula
    K ⁢ ( z , ζ ) 𝐾 𝑧 𝜁 {\displaystyle{\displaystyle K(z,\zeta)}}
    xml-id
    C28.S32.XMD7.m1dec
    0 references
     
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