DLMF:13.18.E13 (Q4582): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Whittaker confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
test:

M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

\WhittakerconfhyperM{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
xml-id: C13.S14.E2.m2agdec
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.m2aedec
Property / Symbols used
 
Property / Symbols used: Q11320 / rank
 
Normal rank
Property / Symbols used: Q11320 / qualifier
 
test:

U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}

\paraU@{\NVar{a}}{\NVar{z}}
Property / Symbols used: Q11320 / qualifier
 
xml-id: C12.S2.SS1.p1.m1abdec

Latest revision as of 15:13, 2 January 2020

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DLMF:13.18.E13
No description defined

    Statements

    test
    M - 1 2 ⁢ a , 1 4 ⁡ ( 1 2 ⁢ z 2 ) = 2 1 2 ⁢ a - 2 ⁢ Γ ⁡ ( 1 2 ⁢ a + 1 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 2 Euler-Gamma 1 2 𝑎 1 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-2}\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{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.E13
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    Whittaker confluent hypergeometric function
    test
    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.m2agdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    Q11320
    test
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1abdec
    0 references
     
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