DLMF:18.18.E3 (Q5793): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11762 / rank
 
Normal rank
Property / Symbols used: Q11762 / qualifier
 
Defining formula:

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

f(z)
Property / Symbols used: Q11762 / qualifier
 
xml-id: C18.S18.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: DLMF:18.18.E1 / rank
 
Normal rank
Property / Symbols used: DLMF:18.18.E1 / qualifier
 
Defining formula:

a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}

a_{n}
Property / Symbols used: DLMF:18.18.E1 / qualifier
 
xml-id: C18.S18.XMD3.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1adec

Latest revision as of 01:21, 2 January 2020

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DLMF:18.18.E3
No description defined

    Statements

    Defining formula
    a n = ( n + 1 2 ) ⁢ ∫ - 1 1 f ⁢ ( x ) ⁢ P n ⁡ ( x ) ⁢ d x . subscript 𝑎 𝑛 𝑛 1 2 superscript subscript 1 1 𝑓 𝑥 shorthand-Legendre-P-first-kind 𝑛 𝑥 𝑥 {\displaystyle{\displaystyle a_{n}=\left(n+\tfrac{1}{2}\right)\int_{-1}^{1}f(x% )P_{n}\left(x\right)\mathrm{d}x.}}
    0 references
    DLMF id
    DLMF:18.18.E3
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q11447
    Defining formula
    P ν ⁡ ( z ) = P ν 0 ⁡ ( z ) shorthand-Legendre-P-first-kind 𝜈 𝑧 Legendre-P-first-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m3adec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1bdec
    0 references
    Q11762
    Defining formula
    f ⁢ ( z ) 𝑓 𝑧 {\displaystyle{\displaystyle f(z)}}
    xml-id
    C18.S18.XMD1.m1bdec
    0 references
    DLMF:18.18.E1
    Defining formula
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C18.S18.XMD3.m1bdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1adec
    0 references
     
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