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DLMF:12.14.E8 - MaRDI portal

DLMF:12.14.E8 (Q4941)

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DLMF:12.14.E8
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    Statements

    DLMF defining formula
    W ⁡ ( a , x ) = W ⁡ ( a , 0 ) ⁢ w 1 ⁢ ( a , x ) + W ′ ⁡ ( a , 0 ) ⁢ w 2 ⁢ ( a , x ) . parabolic-W 𝑎 𝑥 parabolic-W 𝑎 0 subscript 𝑤 1 𝑎 𝑥 diffop parabolic-W 1 𝑎 0 subscript 𝑤 2 𝑎 𝑥 {\displaystyle{\displaystyle W\left(a,x\right)=W\left(a,0\right)w_{1}(a,x)+W'% \left(a,0\right)w_{2}(a,x).}}
    0 references
    Symbols used
    Q11514
    DLMF defining formula
    W ⁡ ( a , x ) parabolic-W 𝑎 𝑥 {\displaystyle{\displaystyle W\left(\NVar{a},\NVar{x}\right)}}
    xml-id
    C12.S14.SS1.p1.m1ahdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C12.S1.XMD1.m1fdec
    0 references
    real or complex parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C12.S1.XMD6.m1fdec
    0 references
    even solution (locally)
    DLMF defining formula
    w 1 ⁢ ( a , x ) subscript 𝑤 1 𝑎 𝑥 {\displaystyle{\displaystyle w_{1}(a,x)}}
    xml-id
    C12.S14.XMD4.m1dec
    0 references
    odd solution (locally)
    DLMF defining formula
    w 2 ⁢ ( a , x ) subscript 𝑤 2 𝑎 𝑥 {\displaystyle{\displaystyle w_{2}(a,x)}}
    xml-id
    C12.S14.XMD5.m1dec
    0 references

    Identifiers

     
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