DLMF:22.13.E21 (Q7072): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
test:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2audec
Property / Symbols used
 
Property / Symbols used: Q11985 / rank
 
Normal rank
Property / Symbols used: Q11985 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11985 / qualifier
 
xml-id: C22.S1.XMD3.m1udec

Latest revision as of 14:21, 2 January 2020

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DLMF:22.13.E21
No description defined

    Statements

    test
    d 2 d z 2 ⁡ sc ⁡ ( z , k ) = ( 1 + k ′ 2 ) ⁢ sc ⁡ ( z , k ) + 2 ⁢ k ′ 2 ⁢ sc 3 ⁡ ( z , k ) , derivative 𝑧 2 Jacobi-elliptic-sc 𝑧 𝑘 1 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sc 𝑧 𝑘 2 superscript superscript 𝑘 ′ 2 Jacobi-elliptic-sc 3 𝑧 𝑘 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}}{{\mathrm{d}z}^{2}}% \operatorname{sc}\left(z,k\right)=(1+{k^{\prime}}^{2})\operatorname{sc}\left(z% ,k\right)+2{k^{\prime}}^{2}{\operatorname{sc}^{3}}\left(z,k\right),}}
    0 references
    DLMF id
    DLMF:22.13.E21
    0 references
    Symbols used
    Jacobian elliptic function
    test
    sc ⁡ ( z , k ) Jacobi-elliptic-sc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m2abdec
    0 references
    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2audec
    0 references
    Q11985
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C22.S1.XMD3.m1udec
    0 references
     
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