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DLMF:28.31.E24 - MaRDI portal

DLMF:28.31.E24 (Q9240)

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DLMF:28.31.E24
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    Statements

    DLMF defining formula
    ∫ u 0 u ∞ ∫ 0 2 ⁢ π ℎ𝑐 p 1 m 1 ⁢ ( u , ξ ) ⁢ ℎ𝑐 p 1 m 1 ⁢ ( v , ξ ) ⁢ ℎ𝑠 p 2 m 2 ⁢ ( u , ξ ) ⁢ ℎ𝑠 p 2 m 2 ⁢ ( v , ξ ) ⁢ ( cos ⁡ ( 2 ⁢ u ) - cos ⁡ ( 2 ⁢ v ) ) ⁢ d v ⁢ d u = 0 , superscript subscript subscript 𝑢 0 subscript 𝑢 superscript subscript 0 2 𝜋 superscript subscript ℎ𝑐 subscript 𝑝 1 subscript 𝑚 1 𝑢 𝜉 superscript subscript ℎ𝑐 subscript 𝑝 1 subscript 𝑚 1 𝑣 𝜉 superscript subscript ℎ𝑠 subscript 𝑝 2 subscript 𝑚 2 𝑢 𝜉 superscript subscript ℎ𝑠 subscript 𝑝 2 subscript 𝑚 2 𝑣 𝜉 2 𝑢 2 𝑣 𝑣 𝑢 0 {\displaystyle{\displaystyle\int_{u_{0}}^{u_{\infty}}\int_{0}^{2\pi}\mathit{hc% }_{p_{1}}^{m_{1}}(u,\xi)\mathit{hc}_{p_{1}}^{m_{1}}(v,\xi)\mathit{hs}_{p_{2}}^% {m_{2}}(u,\xi)\mathit{hs}_{p_{2}}^{m_{2}}(v,\xi)\*\left(\cos\left(2u\right)-% \cos\left(2v\right)\right)\mathrm{d}v\mathrm{d}u=0,}}
    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.m2afdec
    0 references
    cosine function
    DLMF defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2ajdec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1mdec
    0 references
    paraboloidal wave function (locally)
    DLMF defining formula
    ℎ𝑐 p m ⁢ ( z , ξ ) superscript subscript ℎ𝑐 𝑝 𝑚 𝑧 𝜉 {\displaystyle{\displaystyle\mathit{hc}_{p}^{m}(z,\xi)}}
    xml-id
    C28.S31.XMD10.m1edec
    0 references
    paraboloidal wave function (locally)
    DLMF defining formula
    ℎ𝑠 p m ⁢ ( z , ξ ) superscript subscript ℎ𝑠 𝑝 𝑚 𝑧 𝜉 {\displaystyle{\displaystyle\mathit{hs}_{p}^{m}(z,\xi)}}
    xml-id
    C28.S31.XMD11.m1edec
    0 references

    Identifiers

     
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