DLMF:33.2.E1 (Q9496): Difference between revisions

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Property / constraint
 

= 0 , 1 , 2 , 0 1 2 {\displaystyle{\displaystyle\ell=0,1,2,\dots}}

\ell=0,1,2,\dots
Property / constraint: = 0 , 1 , 2 , 0 1 2 {\displaystyle{\displaystyle\ell=0,1,2,\dots}} / rank
 
Normal rank
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q12666 / rank
 
Normal rank
Property / Symbols used: Q12666 / qualifier
 
test:

{\displaystyle{\displaystyle\ell}}

\ell
Property / Symbols used: Q12666 / qualifier
 
xml-id: C33.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q12667 / rank
 
Normal rank
Property / Symbols used: Q12667 / qualifier
 
test:

ρ 𝜌 {\displaystyle{\displaystyle\rho}}

\rho
Property / Symbols used: Q12667 / qualifier
 
xml-id: C33.S1.XMD5.m1dec
Property / Symbols used
 
Property / Symbols used: Q12668 / rank
 
Normal rank
Property / Symbols used: Q12668 / qualifier
 
test:

η 𝜂 {\displaystyle{\displaystyle\eta}}

\eta
Property / Symbols used: Q12668 / qualifier
 
xml-id: C33.S1.XMD7.m1dec

Latest revision as of 13:19, 2 January 2020

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DLMF:33.2.E1
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    Statements

    d 2 w d ρ 2 + ( 1 - 2 η ρ - ( + 1 ) ρ 2 ) w = 0 , derivative 𝑤 𝜌 2 1 2 𝜂 𝜌 1 superscript 𝜌 2 𝑤 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}\rho}^{2}}+% \left(1-\frac{2\eta}{\rho}-\frac{\ell(\ell+1)}{\rho^{2}}\right)w=0,}}
    0 references
    0 references
    = 0 , 1 , 2 , 0 1 2 {\displaystyle{\displaystyle\ell=0,1,2,\dots}}
    0 references
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2adec
    0 references
    {\displaystyle{\displaystyle\ell}}
    C33.S1.XMD2.m1dec
    0 references
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    C33.S1.XMD5.m1dec
    0 references
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    C33.S1.XMD7.m1dec
    0 references