DLMF:22.13.E13 (Q7064): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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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
 
Defining formula:

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.m2amdec
Property / Symbols used
 
Property / Symbols used: Q11985 / rank
 
Normal rank
Property / Symbols used: Q11985 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11985 / qualifier
 
xml-id: C22.S1.XMD3.m1mdec
Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1mdec

Latest revision as of 15:20, 2 January 2020

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DLMF:22.13.E13
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    Statements

    d 2 d z 2 sn ( z , k ) = - ( 1 + k 2 ) sn ( z , k ) + 2 k 2 sn 3 ( z , k ) , derivative 𝑧 2 Jacobi-elliptic-sn 𝑧 𝑘 1 superscript 𝑘 2 Jacobi-elliptic-sn 𝑧 𝑘 2 superscript 𝑘 2 Jacobi-elliptic-sn 3 𝑧 𝑘 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}}{{\mathrm{d}z}^{2}}% \operatorname{sn}\left(z,k\right)=-(1+k^{2})\operatorname{sn}\left(z,k\right)+% 2k^{2}{\operatorname{sn}^{3}}\left(z,k\right),}}
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    DLMF:22.13.E13
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    sn ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E4.m2abdec
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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.m2amdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C22.S1.XMD3.m1mdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1mdec
    0 references