DLMF:12.7.E14 (Q4137): 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:

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

\WhittakerconfhyperW{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
xml-id: C13.S14.E3.m2adec
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.m2aidec
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.m1aidec
Property / Symbols used
 
Property / Symbols used: Q11513 / rank
 
Normal rank
Property / Symbols used: Q11513 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11513 / qualifier
 
xml-id: C12.S1.XMD3.m1mdec
Property / Symbols used
 
Property / Symbols used: Q11516 / rank
 
Normal rank
Property / Symbols used: Q11516 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11516 / qualifier
 
xml-id: C12.S1.XMD6.m1bdec

Latest revision as of 14:13, 2 January 2020

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Language Label Description Also known as
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DLMF:12.7.E14
No description defined

    Statements

    test
    U ⁡ ( a , z ) = 2 - 1 4 - 1 2 ⁢ a ⁢ e - 1 4 ⁢ z 2 ⁢ U ⁡ ( 1 2 ⁢ a + 1 4 , 1 2 , 1 2 ⁢ z 2 ) = 2 - 3 4 - 1 2 ⁢ a ⁢ z ⁢ e - 1 4 ⁢ z 2 ⁢ U ⁡ ( 1 2 ⁢ a + 3 4 , 3 2 , 1 2 ⁢ z 2 ) = 2 - 1 2 ⁢ a ⁢ z - 1 2 ⁢ W - 1 2 ⁢ a , ± 1 4 ⁡ ( 1 2 ⁢ z 2 ) . parabolic-U 𝑎 𝑧 superscript 2 1 4 1 2 𝑎 superscript 𝑒 1 4 superscript 𝑧 2 Kummer-confluent-hypergeometric-U 1 2 𝑎 1 4 1 2 1 2 superscript 𝑧 2 superscript 2 3 4 1 2 𝑎 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 Kummer-confluent-hypergeometric-U 1 2 𝑎 3 4 3 2 1 2 superscript 𝑧 2 superscript 2 1 2 𝑎 superscript 𝑧 1 2 Whittaker-confluent-hypergeometric-W 1 2 𝑎 plus-or-minus 1 4 1 2 superscript 𝑧 2 {\displaystyle{\displaystyle U\left(a,z\right)=2^{-\frac{1}{4}-\frac{1}{2}a}e^% {-\frac{1}{4}z^{2}}U\left(\tfrac{1}{2}a+\tfrac{1}{4},\tfrac{1}{2},\tfrac{1}{2}% z^{2}\right)=2^{-\frac{3}{4}-\frac{1}{2}a}ze^{-\frac{1}{4}z^{2}}U\left(\tfrac{% 1}{2}a+\tfrac{3}{4},\tfrac{3}{2},\tfrac{1}{2}z^{2}\right)=2^{-\frac{1}{2}a}z^{% -\frac{1}{2}}W_{-\frac{1}{2}a,\pm\frac{1}{4}}\left(\tfrac{1}{2}z^{2}\right).}}
    0 references
    DLMF id
    DLMF:12.7.E14
    0 references
    Symbols used
    Kummer confluent hypergeometric function
    test
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2adec
    0 references
    Whittaker confluent hypergeometric function
    test
    W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E3.m2adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
    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.m1aidec
    0 references
    Q11513
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C12.S1.XMD3.m1mdec
    0 references
    Q11516
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C12.S1.XMD6.m1bdec
    0 references
     
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