DLMF:32.10.E33 (Q9434): 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
 
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.m2abdec
Property / Symbols used
 
Property / Symbols used: Q12523 / rank
 
Normal rank
Property / Symbols used: Q12523 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12523 / qualifier
 
xml-id: C32.S1.XMD4.m1xdec
Property / Symbols used
 
Property / Symbols used: Q12627 / rank
 
Normal rank
Property / Symbols used: Q12627 / qualifier
 
Defining formula:

ϕ ( z ) italic-ϕ 𝑧 {\displaystyle{\displaystyle\phi(z)}}

\phi(z)
Property / Symbols used: Q12627 / qualifier
 
xml-id: C32.S10.XMD27.m1bdec

Latest revision as of 14:12, 2 January 2020

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DLMF:32.10.E33
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    Statements

    z ( 1 - z ) d 2 ϕ d z 2 + ( 1 - 2 z ) d ϕ d z - 1 4 ϕ = 0 . 𝑧 1 𝑧 derivative italic-ϕ 𝑧 2 1 2 𝑧 derivative italic-ϕ 𝑧 1 4 italic-ϕ 0 {\displaystyle{\displaystyle z(1-z)\frac{{\mathrm{d}}^{2}\phi}{{\mathrm{d}z}^{% 2}}+(1-2z)\frac{\mathrm{d}\phi}{\mathrm{d}z}-\tfrac{1}{4}\phi=0.}}
    0 references
    DLMF:32.10.E33
    0 references
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2abdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C32.S1.XMD4.m1xdec
    0 references
    ϕ ( z ) italic-ϕ 𝑧 {\displaystyle{\displaystyle\phi(z)}}
    C32.S10.XMD27.m1bdec
    0 references