DLMF:14.5.E27 (Q4739)

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DLMF:14.5.E27
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    Statements

    Defining formula
    𝑸 - 1 2 ⁑ ( cosh ⁑ ΞΎ ) = 2 ⁒ Ο€ - 1 / 2 ⁒ e - ΞΎ / 2 ⁒ K ⁑ ( e - ΞΎ ) . shorthand-associated-Legendre-black-Q 1 2 πœ‰ 2 superscript πœ‹ 1 2 superscript 𝑒 πœ‰ 2 complete-elliptic-integral-first-kind-K superscript 𝑒 πœ‰ {\displaystyle{\displaystyle\boldsymbol{Q}_{-\frac{1}{2}}\left(\cosh\xi\right)% =2\pi^{-1/2}e^{-\xi/2}K\left(e^{-\xi}\right).}}
    0 references
    DLMF id
    DLMF:14.5.E27
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    Ο€ {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2apdec
    0 references
    Q11600
    Defining formula
    K ⁑ ( k ) complete-elliptic-integral-first-kind-K π‘˜ {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1afdec
    0 references
     
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