DLMF:14.5.E26 (Q4738)

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DLMF:14.5.E26
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    Statements

    test
    𝑸 1 2 ⁑ ( cosh ⁑ ΞΎ ) = 2 ⁒ Ο€ - 1 / 2 ⁒ cosh ⁑ ΞΎ ⁒ sech ⁑ ( 1 2 ⁒ ΞΎ ) ⁒ K ⁑ ( sech ⁑ ( 1 2 ⁒ ΞΎ ) ) - 4 ⁒ Ο€ - 1 / 2 ⁒ cosh ⁑ ( 1 2 ⁒ ΞΎ ) ⁒ E ⁑ ( sech ⁑ ( 1 2 ⁒ ΞΎ ) ) , shorthand-associated-Legendre-black-Q 1 2 πœ‰ 2 superscript πœ‹ 1 2 πœ‰ 1 2 πœ‰ complete-elliptic-integral-first-kind-K 1 2 πœ‰ 4 superscript πœ‹ 1 2 1 2 πœ‰ complete-elliptic-integral-second-kind-E 1 2 πœ‰ {\displaystyle{\displaystyle\boldsymbol{Q}_{\frac{1}{2}}\left(\cosh\xi\right)=% 2\pi^{-1/2}\cosh\xi\operatorname{sech}\left(\tfrac{1}{2}\xi\right)K\left(% \operatorname{sech}\left(\tfrac{1}{2}\xi\right)\right)-4\pi^{-1/2}\cosh\left(% \tfrac{1}{2}\xi\right)E\left(\operatorname{sech}\left(\tfrac{1}{2}\xi\right)% \right),}}
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    DLMF id
    DLMF:14.5.E26
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