DLMF:12.2.E12 (Q4097): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11513 / rank
 
Normal rank
Property / Symbols used: Q11513 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11513 / qualifier
 
xml-id: C12.S1.XMD3.m1gdec

Revision as of 15:05, 2 January 2020

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DLMF:12.2.E12
No description defined

    Statements

    Defining formula
    𝒲 ⁡ { U ⁡ ( a , z ) , U ⁡ ( - a , ± i ⁢ z ) } = ∓ i ⁢ e ± i ⁢ π ⁢ ( 1 2 ⁢ a + 1 4 ) . Wronskian parabolic-U 𝑎 𝑧 parabolic-U 𝑎 plus-or-minus 𝑖 𝑧 minus-or-plus 𝑖 superscript 𝑒 plus-or-minus 𝑖 𝜋 1 2 𝑎 1 4 {\displaystyle{\displaystyle\mathscr{W}\left\{U\left(a,z\right),U\left(-a,\pm iz% \right)\right\}=\mp ie^{\pm i\pi(\frac{1}{2}a+\frac{1}{4})}.}}
    0 references
    DLMF id
    DLMF:12.2.E12
    0 references
    Symbols used
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.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.m1aedec
    0 references
    Q11513
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C12.S1.XMD3.m1gdec
    0 references
     
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