DLMF:13.14.E4 (Q4493): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function / qualifier
 
test:

M ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}

\KummerconfhyperM@{\NVar{a}}{\NVar{b}}{\NVar{z}}
Property / Symbols used: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function / qualifier
 
xml-id: C13.S2.E2.m2aadec
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.m2aadec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1cdec

Latest revision as of 15:05, 2 January 2020

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DLMF:13.14.E4
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    Statements

    test
    M ⁡ ( a , b , z ) = e 1 2 ⁢ z ⁢ z - 1 2 ⁢ b ⁢ M 1 2 ⁢ b - a , 1 2 ⁢ b - 1 2 ⁡ ( z ) , Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 superscript 𝑒 1 2 𝑧 superscript 𝑧 1 2 𝑏 Whittaker-confluent-hypergeometric-M 1 2 𝑏 𝑎 1 2 𝑏 1 2 𝑧 {\displaystyle{\displaystyle M\left(a,b,z\right)=e^{\frac{1}{2}z}z^{-\frac{1}{% 2}b}M_{\frac{1}{2}b-a,\frac{1}{2}b-\frac{1}{2}}\left(z\right),}}
    0 references
    DLMF id
    DLMF:13.14.E4
    0 references
    Symbols used
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    test
    M ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E2.m2aadec
    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.m2aadec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    Q11557
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1cdec
    0 references
    Q11557
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1cdec
    0 references
     
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