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DLMF:13.9.E8 - MaRDI portal

DLMF:13.9.E8 (Q5148)

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DLMF:13.9.E8
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    Statements

    DLMF defining formula
    ϕ r = j b - 1 , r 2 2 ⁢ b - 4 ⁢ a ⁢ ( 1 + 2 ⁢ b ⁢ ( b - 2 ) + j b - 1 , r 2 3 ⁢ ( 2 ⁢ b - 4 ⁢ a ) 2 ) + O ⁡ ( 1 a 5 ) , subscript italic-ϕ 𝑟 superscript subscript 𝑗 𝑏 1 𝑟 2 2 𝑏 4 𝑎 1 2 𝑏 𝑏 2 superscript subscript 𝑗 𝑏 1 𝑟 2 3 superscript 2 𝑏 4 𝑎 2 Big-O 1 superscript 𝑎 5 {\displaystyle{\displaystyle\phi_{r}=\frac{j_{b-1,r}^{2}}{2b-4a}\left(1+\frac{% 2b(b-2)+j_{b-1,r}^{2}}{3(2b-4a)^{2}}\right)+O\left(\frac{1}{a^{5}}\right),}}
    0 references
    Symbols used
    order not exceeding
    DLMF defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    = r 1 , 2 , 3 , …
    DLMF defining formula
    r = 1 , 2 , 3 , … 𝑟 1 2 3 … {\displaystyle{\displaystyle r=1,2,3,\dots}}
    xml-id
    C13.S9.XMD3.m1dec
    0 references
    positive zeros
    DLMF defining formula
    ϕ r subscript italic-ϕ 𝑟 {\displaystyle{\displaystyle\phi_{r}}}
    xml-id
    C13.S9.XMD4.m1dec
    0 references
    positive zero of Bessel
    DLMF defining formula
    j b , r subscript 𝑗 𝑏 𝑟 {\displaystyle{\displaystyle j_{b,r}}}
    xml-id
    C13.S9.XMD5.m1dec
    0 references

    Identifiers

     
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