DLMF:32.2.E5 (Q9158): 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.m2addec
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.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12524 / rank
 
Normal rank
Property / Symbols used: Q12524 / qualifier
 
Defining formula:

α 𝛼 {\displaystyle{\displaystyle\alpha}}

\alpha
Property / Symbols used: Q12524 / qualifier
 
xml-id: C32.S2.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12525 / rank
 
Normal rank
Property / Symbols used: Q12525 / qualifier
 
Defining formula:

β 𝛽 {\displaystyle{\displaystyle\beta}}

\beta
Property / Symbols used: Q12525 / qualifier
 
xml-id: C32.S2.XMD2.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12526 / rank
 
Normal rank
Property / Symbols used: Q12526 / qualifier
 
Defining formula:

γ 𝛾 {\displaystyle{\displaystyle\gamma}}

\gamma
Property / Symbols used: Q12526 / qualifier
 
xml-id: C32.S2.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q12527 / rank
 
Normal rank
Property / Symbols used: Q12527 / qualifier
 
Defining formula:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q12527 / qualifier
 
xml-id: C32.S2.XMD4.m1adec

Latest revision as of 13:48, 2 January 2020

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English
DLMF:32.2.E5
No description defined

    Statements

    Defining formula
    d 2 w d z 2 = ( 1 2 ⁢ w + 1 w - 1 ) ⁢ ( d w d z ) 2 - 1 z ⁢ d w d z + ( w - 1 ) 2 z 2 ⁢ ( α ⁢ w + β w ) + γ ⁢ w z + δ ⁢ w ⁢ ( w + 1 ) w - 1 , derivative 𝑤 𝑧 2 1 2 𝑤 1 𝑤 1 superscript derivative 𝑤 𝑧 2 1 𝑧 derivative 𝑤 𝑧 superscript 𝑤 1 2 superscript 𝑧 2 𝛼 𝑤 𝛽 𝑤 𝛾 𝑤 𝑧 𝛿 𝑤 𝑤 1 𝑤 1 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=\left(% \frac{1}{2w}+\frac{1}{w-1}\right)\left(\frac{\mathrm{d}w}{\mathrm{d}z}\right)^% {2}-\frac{1}{z}\frac{\mathrm{d}w}{\mathrm{d}z}+\frac{(w-1)^{2}}{z^{2}}\left(% \alpha w+\frac{\beta}{w}\right)+\frac{\gamma w}{z}+\frac{\delta w(w+1)}{w-1},}}
    0 references
    DLMF id
    DLMF:32.2.E5
    0 references
    Symbols used
    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2addec
    0 references
    Q12523
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C32.S1.XMD4.m1ddec
    0 references
    Q12524
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C32.S2.XMD1.m1cdec
    0 references
    Q12525
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C32.S2.XMD2.m1bdec
    0 references
    Q12526
    Defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C32.S2.XMD3.m1adec
    0 references
    Q12527
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C32.S2.XMD4.m1adec
    0 references
     
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