DLMF:12.14.E15 (Q4255): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: even solution (locally) / rank
 
Normal rank
Property / Symbols used: even solution (locally) / qualifier
 
Defining formula:

w 1 ⁢ ( a , x ) subscript 𝑤 1 𝑎 𝑥 {\displaystyle{\displaystyle w_{1}(a,x)}}

w_{1}(a,x)
Property / Symbols used: even solution (locally) / qualifier
 
xml-id: C12.S14.XMD4.m1bdec

Latest revision as of 15:28, 2 January 2020

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DLMF:12.14.E15
No description defined

    Statements

    Defining formula
    w 1 ⁢ ( a , x ) = e - 1 4 ⁢ i ⁢ x 2 ⁢ M ⁡ ( 1 4 - 1 2 ⁢ i ⁢ a , 1 2 , 1 2 ⁢ i ⁢ x 2 ) = e 1 4 ⁢ i ⁢ x 2 ⁢ M ⁡ ( 1 4 + 1 2 ⁢ i ⁢ a , 1 2 , - 1 2 ⁢ i ⁢ x 2 ) , subscript 𝑤 1 𝑎 𝑥 superscript 𝑒 1 4 𝑖 superscript 𝑥 2 Kummer-confluent-hypergeometric-M 1 4 1 2 𝑖 𝑎 1 2 1 2 𝑖 superscript 𝑥 2 superscript 𝑒 1 4 𝑖 superscript 𝑥 2 Kummer-confluent-hypergeometric-M 1 4 1 2 𝑖 𝑎 1 2 1 2 𝑖 superscript 𝑥 2 {\displaystyle{\displaystyle w_{1}(a,x)=e^{-\frac{1}{4}ix^{2}}M\left(\tfrac{1}% {4}-\tfrac{1}{2}ia,\tfrac{1}{2},\tfrac{1}{2}ix^{2}\right)=e^{\frac{1}{4}ix^{2}% }M\left(\tfrac{1}{4}+\tfrac{1}{2}ia,\tfrac{1}{2},-\tfrac{1}{2}ix^{2}\right),}}
    0 references
    DLMF id
    DLMF:12.14.E15
    0 references
    Symbols used
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    Defining formula
    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.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    Q11520
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C12.S1.XMD1.m1kdec
    0 references
    Q11516
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C12.S1.XMD6.m1kdec
    0 references
    even solution (locally)
    Defining formula
    w 1 ⁢ ( a , x ) subscript 𝑤 1 𝑎 𝑥 {\displaystyle{\displaystyle w_{1}(a,x)}}
    xml-id
    C12.S14.XMD4.m1bdec
    0 references
     
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