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DLMF:19.2.E11 - MaRDI portal

DLMF:19.2.E11 (Q6795)

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DLMF:19.2.E11
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    Statements

    DLMF defining formula
    cel ⁡ ( k c , p , a , b ) = ∫ 0 π / 2 a ⁢ cos 2 ⁡ θ + b ⁢ sin 2 ⁡ θ cos 2 ⁡ θ + p ⁢ sin 2 ⁡ θ ⁢ d θ cos 2 ⁡ θ + k c 2 ⁢ sin 2 ⁡ θ , Bulirsch-integral-cel subscript 𝑘 𝑐 𝑝 𝑎 𝑏 superscript subscript 0 𝜋 2 𝑎 2 𝜃 𝑏 2 𝜃 2 𝜃 𝑝 2 𝜃 𝜃 2 𝜃 superscript subscript 𝑘 𝑐 2 2 𝜃 {\displaystyle{\displaystyle\mathrm{cel}\left(k_{c},p,a,b\right)=\int_{0}^{\pi% /2}\frac{a{\cos^{2}}\theta+b{\sin^{2}}\theta}{{\cos^{2}}\theta+p{\sin^{2}}% \theta}\frac{\mathrm{d}\theta}{\sqrt{{\cos^{2}}\theta+k_{c}^{2}{\sin^{2}}% \theta}},}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    cosine function
    DLMF defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
    0 references
    sine function
    DLMF defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2addec
    0 references
    polynomial
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C19.S2.XMD4.m1dec
    0 references
    real parameter
    DLMF defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C19.S2.XMD5.m1dec
    0 references
    real parameter
    DLMF defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C19.S2.XMD6.m1dec
    0 references
    real parameter not equal to zero
    DLMF defining formula
    k c subscript 𝑘 𝑐 {\displaystyle{\displaystyle k_{c}}}
    xml-id
    C19.S2.XMD7.m1dec
    0 references

    Identifiers

     
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