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DLMF:9.4.E1 - MaRDI portal

DLMF:9.4.E1 (Q3467)

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DLMF:9.4.E1
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    Statements

    DLMF defining formula
    Ai ⁡ ( z ) = Ai ⁡ ( 0 ) ⁢ ( 1 + 1 3 ! ⁢ z 3 + 1 ⋅ 4 6 ! ⁢ z 6 + 1 ⋅ 4 ⋅ 7 9 ! ⁢ z 9 + ⋯ ) + Ai ′ ⁡ ( 0 ) ⁢ ( z + 2 4 ! ⁢ z 4 + 2 ⋅ 5 7 ! ⁢ z 7 + 2 ⋅ 5 ⋅ 8 10 ! ⁢ z 10 + ⋯ ) , Airy-Ai 𝑧 Airy-Ai 0 1 1 3 superscript 𝑧 3 ⋅ 1 4 6 superscript 𝑧 6 ⋅ 1 4 7 9 superscript 𝑧 9 ⋯ diffop Airy-Ai 1 0 𝑧 2 4 superscript 𝑧 4 ⋅ 2 5 7 superscript 𝑧 7 ⋅ 2 5 8 10 superscript 𝑧 10 ⋯ {\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\mathrm{Ai}\left(0\right% )\left(1+\frac{1}{3!}z^{3}+\frac{1\cdot 4}{6!}z^{6}+\frac{1\cdot 4\cdot 7}{9!}% z^{9}+\cdots\right)+\mathrm{Ai}'\left(0\right)\left(z+\frac{2}{4!}z^{4}+\frac{% 2\cdot 5}{7!}z^{7}+\frac{2\cdot 5\cdot 8}{10!}z^{10}+\cdots\right),}}
    0 references
    Symbols used
    Q10893
    DLMF defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1adec
    0 references
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1dec
    0 references

    Identifiers

     
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