DLMF:29.14.E1 (Q8735): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11600 / rank
 
Normal rank
Property / Symbols used: Q11600 / qualifier
 
Defining formula:

K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}

\compellintKk@{\NVar{k}}
Property / Symbols used: Q11600 / qualifier
 
xml-id: C19.S2.E8.m1adec

Revision as of 01:27, 2 January 2020

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DLMF:29.14.E1
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    Statements

    Defining formula
    f n m ⁢ ( s , t ) = 𝑢𝐸 2 ⁢ n m ⁡ ( s , k 2 ) ⁢ 𝑢𝐸 2 ⁢ n m ⁡ ( K ⁡ + i ⁢ t , k 2 ) , superscript subscript 𝑓 𝑛 𝑚 𝑠 𝑡 Lame-polynomial-uE 𝑚 2 𝑛 𝑠 superscript 𝑘 2 Lame-polynomial-uE 𝑚 2 𝑛 complete-elliptic-integral-first-kind-K 𝑘 imaginary-unit 𝑡 superscript 𝑘 2 {\displaystyle{\displaystyle f_{n}^{m}(s,t)=\mathit{uE}^{m}_{2n}\left(s,k^{2}% \right)\mathit{uE}^{m}_{2n}\left(K+\mathrm{i}t,k^{2}\right),}}
    0 references
    DLMF id
    DLMF:29.14.E1
    0 references
    constraint
    m = 0 , 1 , … , n 𝑚 0 1 … 𝑛 {\displaystyle{\displaystyle m=0,1,\dots,n}}
    0 references
    Symbols used
    Lamé polynomial
    Defining formula
    𝑢𝐸 2 ⁢ n m ⁡ ( z , k 2 ) Lame-polynomial-uE 𝑚 2 𝑛 𝑧 superscript 𝑘 2 {\displaystyle{\displaystyle\mathit{uE}^{\NVar{m}}_{2\NVar{n}}\left(\NVar{z},% \NVar{k^{2}}\right)}}
    xml-id
    C29.S12.E1.m2adec
    0 references
    Q11600
    Defining formula
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1adec
    0 references
     
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