DLMF:12.2.E20 (Q4105): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aldec

Revision as of 14:06, 2 January 2020

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DLMF:12.2.E20
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    Statements

    test
    V ⁡ ( a , z ) = ∓ i Γ ⁡ ( 1 2 - a ) ⁢ U ⁡ ( a , z ) + 2 π ⁢ e ∓ i ⁢ π ⁢ ( 1 2 ⁢ a - 1 4 ) ⁢ U ⁡ ( - a , ± i ⁢ z ) . parabolic-V 𝑎 𝑧 minus-or-plus 𝑖 Euler-Gamma 1 2 𝑎 parabolic-U 𝑎 𝑧 2 𝜋 superscript 𝑒 minus-or-plus 𝑖 𝜋 1 2 𝑎 1 4 parabolic-U 𝑎 plus-or-minus 𝑖 𝑧 {\displaystyle{\displaystyle V\left(a,z\right)=\frac{\mp i}{\Gamma\left(\frac{% 1}{2}-a\right)}U\left(a,z\right)+\sqrt{\frac{2}{\pi}}e^{\mp i\pi(\frac{1}{2}a-% \frac{1}{4})}U\left(-a,\pm iz\right).}}
    0 references
    DLMF id
    DLMF:12.2.E20
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ajdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aldec
    0 references
     
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