DLMF:29.15.E23 (Q8768): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12367 / rank
 
Normal rank
Property / Symbols used: Q12367 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12367 / qualifier
 
xml-id: C29.S1.XMD2.m1rdec
Property / Symbols used
 
Property / Symbols used: Q12359 / rank
 
Normal rank
Property / Symbols used: Q12359 / qualifier
 
Defining formula:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: Q12359 / qualifier
 
xml-id: C29.S1.XMD3.m1ldec
Property / Symbols used
 
Property / Symbols used: Q12348 / rank
 
Normal rank
Property / Symbols used: Q12348 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12348 / qualifier
 
xml-id: C29.S1.XMD6.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12350 / rank
 
Normal rank
Property / Symbols used: Q12350 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12350 / qualifier
 
xml-id: C29.S1.XMD8.m1idec
Property / Symbols used
 
Property / Symbols used: change of variable (locally) / rank
 
Normal rank
Property / Symbols used: change of variable (locally) / qualifier
 
Defining formula:

ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}

\phi
Property / Symbols used: change of variable (locally) / qualifier
 
xml-id: C29.S2.XMD3.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12374 / rank
 
Normal rank
Property / Symbols used: Q12374 / qualifier
 
Defining formula:

B 2 ⁢ p + 1 subscript 𝐵 2 𝑝 1 {\displaystyle{\displaystyle B_{2p+1}}}

B_{2p+1}
Property / Symbols used: Q12374 / qualifier
 
xml-id: C29.S6.XMD12.m1ddec

Latest revision as of 01:33, 2 January 2020

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English
DLMF:29.15.E23
No description defined

    Statements

    Defining formula
    𝑠𝑐𝐸 2 ⁢ n + 2 m ⁡ ( z , k 2 ) = ∑ p = 0 n B 2 ⁢ p + 2 ⁢ sin ⁡ ( ( 2 ⁢ p + 2 ) ⁢ ϕ ) . Lame-polynomial-scE 𝑚 2 𝑛 2 𝑧 superscript 𝑘 2 superscript subscript 𝑝 0 𝑛 subscript 𝐵 2 𝑝 2 2 𝑝 2 italic-ϕ {\displaystyle{\displaystyle\mathit{scE}^{m}_{2n+2}\left(z,k^{2}\right)=\sum_{% p=0}^{n}B_{2p+2}\sin\left((2p+2)\phi\right).}}
    0 references
    DLMF id
    DLMF:29.15.E23
    0 references
    Symbols used
    Lamé polynomial
    Defining formula
    𝑠𝑐𝐸 2 ⁢ n + 2 m ⁡ ( z , k 2 ) Lame-polynomial-scE 𝑚 2 𝑛 2 𝑧 superscript 𝑘 2 {\displaystyle{\displaystyle\mathit{scE}^{\NVar{m}}_{2\NVar{n}+2}\left(\NVar{z% },\NVar{k^{2}}\right)}}
    xml-id
    C29.S12.E5.m2adec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    Q12357
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C29.S1.XMD1.m1hdec
    0 references
    Q12367
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C29.S1.XMD2.m1rdec
    0 references
    Q12359
    Defining formula
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C29.S1.XMD3.m1ldec
    0 references
    Q12348
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C29.S1.XMD6.m1ddec
    0 references
    Q12350
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C29.S1.XMD8.m1idec
    0 references
    change of variable (locally)
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C29.S2.XMD3.m1ddec
    0 references
    Q12374
    Defining formula
    B 2 ⁢ p + 1 subscript 𝐵 2 𝑝 1 {\displaystyle{\displaystyle B_{2p+1}}}
    xml-id
    C29.S6.XMD12.m1ddec
    0 references
     
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