DLMF:32.10.E19 (Q9419): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12614 / rank
 
Normal rank
Property / Symbols used: Q12614 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12614 / qualifier
 
xml-id: C32.S10.XMD12.m1dec

Revision as of 14:10, 2 January 2020

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DLMF:32.10.E19
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    Statements

    Defining formula
    ϕ ⁢ ( z ) = ( C 1 ⁢ U ⁡ ( a , 2 ⁢ z ) + C 2 ⁢ V ⁡ ( a , 2 ⁢ z ) ) ⁢ exp ⁡ ( 1 2 ⁢ ε ⁢ z 2 ) , italic-ϕ 𝑧 subscript 𝐶 1 parabolic-U 𝑎 2 𝑧 subscript 𝐶 2 parabolic-V 𝑎 2 𝑧 1 2 𝜀 superscript 𝑧 2 {\displaystyle{\displaystyle\phi(z)=\left(C_{1}U\left(a,\sqrt{2}z\right)+C_{2}% V\left(a,\sqrt{2}z\right)\right)\exp\left(\tfrac{1}{2}\varepsilon z^{2}\right)% ,}}
    0 references
    DLMF id
    DLMF:32.10.E19
    0 references
    Symbols used
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
    0 references
    Q11320
    Defining formula
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1adec
    0 references
    Q11517
    Defining formula
    V ⁡ ( a , z ) parabolic-V 𝑎 𝑧 {\displaystyle{\displaystyle V\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m2adec
    0 references
    Q12523
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C32.S1.XMD4.m1ndec
    0 references
    Q12612
    Defining formula
    ε = ± 1 𝜀 plus-or-minus 1 {\displaystyle{\displaystyle\varepsilon=\pm 1}}
    xml-id
    C32.S10.XMD10.m1cdec
    0 references
    Q12613
    Defining formula
    ϕ ⁢ ( z ) italic-ϕ 𝑧 {\displaystyle{\displaystyle\phi(z)}}
    xml-id
    C32.S10.XMD11.m1adec
    0 references
    Q12614
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C32.S10.XMD12.m1dec
    0 references
     
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