DLMF:22.13.E18 (Q7069): 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.m2ardec
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.m1rdec
Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1rdec
Property / Symbols used
 
Property / Symbols used: Q11988 / rank
 
Normal rank
Property / Symbols used: Q11988 / qualifier
 
test:

k superscript 𝑘 {\displaystyle{\displaystyle k^{\prime}}}

k^{\prime}
Property / Symbols used: Q11988 / qualifier
 
xml-id: C22.S1.XMD5.m1ldec

Latest revision as of 14:21, 2 January 2020

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DLMF:22.13.E18
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    Statements

    d 2 d z 2 nd ( z , k ) = ( 1 + k 2 ) nd ( z , k ) - 2 k 2 nd 3 ( z , k ) , derivative 𝑧 2 Jacobi-elliptic-nd 𝑧 𝑘 1 superscript superscript 𝑘 2 Jacobi-elliptic-nd 𝑧 𝑘 2 superscript superscript 𝑘 2 Jacobi-elliptic-nd 3 𝑧 𝑘 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}}{{\mathrm{d}z}^{2}}% \operatorname{nd}\left(z,k\right)=(1+{k^{\prime}}^{2})\operatorname{nd}\left(z% ,k\right)-2{k^{\prime}}^{2}{\operatorname{nd}^{3}}\left(z,k\right),}}
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    nd ( z , k ) Jacobi-elliptic-nd 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nd}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E6.m3abdec
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    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2ardec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C22.S1.XMD3.m1rdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1rdec
    0 references
    k superscript 𝑘 {\displaystyle{\displaystyle k^{\prime}}}
    C22.S1.XMD5.m1ldec
    0 references