DLMF:23.6.E29 (Q7272): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11821 / rank
 
Normal rank
Property / Symbols used: Q11821 / qualifier
 
Defining formula:

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

\ccompellintKk@{\NVar{k}}
Property / Symbols used: Q11821 / qualifier
 
xml-id: C19.S2.E9.m1aadec

Revision as of 15:52, 2 January 2020

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DLMF:23.6.E29
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    Statements

    ζ ( z | 𝕃 3 ) - ζ ( z + 2 i K | 𝕃 3 ) - ζ ( 2 i K | 𝕃 3 ) = cs ( z , k ) . Weierstrass-zeta-on-lattice 𝑧 subscript 𝕃 3 Weierstrass-zeta-on-lattice 𝑧 2 imaginary-unit complementary-complete-elliptic-integral-first-kind-K 𝑘 subscript 𝕃 3 Weierstrass-zeta-on-lattice 2 imaginary-unit complementary-complete-elliptic-integral-first-kind-K 𝑘 subscript 𝕃 3 Jacobi-elliptic-cs 𝑧 𝑘 {\displaystyle{\displaystyle\zeta\left(z|\mathbb{L}_{\mspace{1.0mu }3}\right)-% \zeta\left(z+2\mathrm{i}{K^{\prime}}|\mathbb{L}_{\mspace{1.0mu }3}\right)-% \zeta\left(2\mathrm{i}{K^{\prime}}|\mathbb{L}_{\mspace{1.0mu }3}\right)=% \operatorname{cs}\left(z,k\right).}}
    0 references
    DLMF:23.6.E29
    0 references
    cs ( z , k ) Jacobi-elliptic-cs 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cs}\left(\NVar{z},\NVar{k}\right)}}
    C22.S2.E9.m3aadec
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    ζ ( z ) Weierstrass-zeta-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}
    C23.S2.E5.m2acdec
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    K ( k ) complementary-complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle{K^{\prime}}\left(\NVar{k}\right)}}
    C19.S2.E9.m1aadec
    0 references