DLMF:22.20.E4 (Q7189)

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DLMF:22.20.E4
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    Statements

    Defining formula
    ϕ n - 1 = 1 2 ⁢ ( ϕ n + arcsin ⁡ ( c n a n ⁢ sin ⁡ ϕ n ) ) , subscript italic-ϕ 𝑛 1 1 2 subscript italic-ϕ 𝑛 subscript 𝑐 𝑛 subscript 𝑎 𝑛 subscript italic-ϕ 𝑛 {\displaystyle{\displaystyle\phi_{n-1}=\frac{1}{2}\left(\phi_{n}+\operatorname% {arcsin}\left(\frac{c_{n}}{a_{n}}\sin\phi_{n}\right)\right),}}
    0 references
    DLMF id
    DLMF:22.20.E4
    0 references
    Symbols used
    Q11242
    Defining formula
    arcsin ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arcsin}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m5adec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    Q12043
    Defining formula
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C22.S20.XMD1.m1cdec
    0 references
    Q12045
    Defining formula
    c n subscript 𝑐 𝑛 {\displaystyle{\displaystyle c_{n}}}
    xml-id
    C22.S20.XMD3.m1bdec
    0 references
    Q12046
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C22.S20.XMD4.m1bdec
    0 references
    Q12048
    Defining formula
    ϕ N subscript italic-ϕ 𝑁 {\displaystyle{\displaystyle\phi_{N}}}
    xml-id
    C22.S20.XMD6.m1adec
    0 references
     
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