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DLMF:18.9.E8 - MaRDI portal

DLMF:18.9.E8 (Q6301)

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DLMF:18.9.E8
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    Statements

    DLMF defining formula
    4 ⁢ λ ⁢ ( n + λ + 1 ) ⁢ ( 1 - x 2 ) ⁢ C n ( λ + 1 ) ⁡ ( x ) = - ( n + 1 ) ⁢ ( n + 2 ) ⁢ C n + 2 ( λ ) ⁡ ( x ) + ( n + 2 ⁢ λ ) ⁢ ( n + 2 ⁢ λ + 1 ) ⁢ C n ( λ ) ⁡ ( x ) . 4 𝜆 𝑛 𝜆 1 1 superscript 𝑥 2 ultraspherical-Gegenbauer-polynomial 𝜆 1 𝑛 𝑥 𝑛 1 𝑛 2 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 2 𝑥 𝑛 2 𝜆 𝑛 2 𝜆 1 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle 4\lambda(n+\lambda+1)(1-x^{2})C^{(\lambda+1)}_{n}% \left(x\right)=-(n+1)(n+2)C^{(\lambda)}_{n+2}\left(x\right)+(n+2\lambda)(n+2% \lambda+1)C^{(\lambda)}_{n}\left(x\right).}}
    0 references
    Symbols used
    ultraspherical (or Gegenbauer) polynomial
    DLMF defining formula
    C n ( λ ) ⁡ ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r3.m2abdec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1hdec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1gdec
    0 references

    Identifiers

     
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