DLMF:2.10.E33 (Q1020): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10769 / rank
 
Normal rank
Property / Symbols used: Q10769 / qualifier
 
test:

≡ equal-by definition {\displaystyle{\displaystyle\equiv}}

\defeq
Property / Symbols used: Q10769 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r9.m2adec
Property / Symbols used
 
Property / Symbols used: Q11127 / rank
 
Normal rank
Property / Symbols used: Q11127 / qualifier
 
test:

f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}

f(x)
Property / Symbols used: Q11127 / qualifier
 
xml-id: C2.S10.XMD13.m1edec

Latest revision as of 16:37, 1 January 2020

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DLMF:2.10.E33
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    Statements

    test
    f ⁢ ( z ) ≡ 1 ( 1 - 2 ⁢ z ⁢ cos ⁡ α + z 2 ) 1 / 2 = ∑ n = 0 ∞ P n ⁡ ( cos ⁡ α ) ⁢ z n , equal-by definition 𝑓 𝑧 1 superscript 1 2 𝑧 𝛼 superscript 𝑧 2 1 2 superscript subscript 𝑛 0 Legendre-spherical-polynomial 𝑛 𝛼 superscript 𝑧 𝑛 {\displaystyle{\displaystyle f(z)\equiv\frac{1}{(1-2z\cos\alpha+z^{2})^{1/2}}=% \sum_{n=0}^{\infty}P_{n}\left(\cos\alpha\right)z^{n},}}
    0 references
    DLMF id
    DLMF:2.10.E33
    0 references
    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    Symbols used
    Q10920
    test
    P n ⁡ ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r10.m2adec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    Q10769
    test
    ≡ equal-by definition {\displaystyle{\displaystyle\equiv}}
    xml-id
    introduction.Sx4.p1.t1.r9.m2adec
    0 references
    Q11127
    test
    f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}
    xml-id
    C2.S10.XMD13.m1edec
    0 references
     
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