DLMF:12.7.E12 (Q4135): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11513 / rank
 
Normal rank
Property / Symbols used: Q11513 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11513 / qualifier
 
xml-id: C12.S1.XMD3.m1kdec

Revision as of 15:13, 2 January 2020

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DLMF:12.7.E12
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    Statements

    u 1 ( a , z ) = e - 1 4 z 2 M ( 1 2 a + 1 4 , 1 2 , 1 2 z 2 ) = e 1 4 z 2 M ( - 1 2 a + 1 4 , 1 2 , - 1 2 z 2 ) , subscript 𝑢 1 𝑎 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 Kummer-confluent-hypergeometric-M 1 2 𝑎 1 4 1 2 1 2 superscript 𝑧 2 superscript 𝑒 1 4 superscript 𝑧 2 Kummer-confluent-hypergeometric-M 1 2 𝑎 1 4 1 2 1 2 superscript 𝑧 2 {\displaystyle{\displaystyle u_{1}(a,z)=e^{-\tfrac{1}{4}z^{2}}M\left(\tfrac{1}% {2}a+\tfrac{1}{4},\tfrac{1}{2},\tfrac{1}{2}z^{2}\right)=e^{\tfrac{1}{4}z^{2}}M% \left(-\tfrac{1}{2}a+\tfrac{1}{4},\tfrac{1}{2},-\tfrac{1}{2}z^{2}\right),}}
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    DLMF:12.7.E12
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    M ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    C13.S2.E2.m2adec
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    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2agdec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C12.S1.XMD3.m1kdec
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