DLMF:13.18.E12 (Q4581): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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
 
Defining formula:

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.m2addec

Revision as of 16:13, 2 January 2020

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DLMF:13.18.E12
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    Statements

    Defining formula
    M - 1 2 ⁢ a , - 1 4 ⁡ ( 1 2 ⁢ z 2 ) = 2 1 2 ⁢ a - 1 ⁢ Γ ⁡ ( 1 2 ⁢ a + 3 4 ) ⁢ z / π ⁢ ( U ⁡ ( a , z ) + U ⁡ ( a , - z ) ) , Whittaker-confluent-hypergeometric-M 1 2 𝑎 1 4 1 2 superscript 𝑧 2 superscript 2 1 2 𝑎 1 Euler-Gamma 1 2 𝑎 3 4 𝑧 𝜋 parabolic-U 𝑎 𝑧 parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle M_{-\frac{1}{2}a,-\frac{1}{4}}\left(\tfrac{1}{2}z% ^{2}\right)=2^{\frac{1}{2}a-1}\Gamma\left(\tfrac{1}{2}a+\tfrac{3}{4}\right)% \sqrt{\ifrac{z}{\pi}}\*\left(U\left(a,z\right)+U\left(a,-z\right)\right),}}
    0 references
    DLMF id
    DLMF:13.18.E12
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Whittaker confluent hypergeometric function
    Defining formula
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2afdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
     
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