DLMF:14.5.E27 (Q4739)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:14.5.E27
No description defined

    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
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁑ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2agdec
    0 references
    Q11597
    Defining formula
    𝑸 Ξ½ ⁑ ( z ) = 𝑸 Ξ½ 0 ⁑ ( z ) shorthand-associated-Legendre-black-Q 𝜈 𝑧 associated-Legendre-black-Q 0 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}_{\NVar{\nu}}\left(\NVar{z}\right)=% \boldsymbol{Q}^{0}_{\nu}\left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m6acdec
    0 references
    Q11599
    Defining formula
    ΞΎ > 0 πœ‰ 0 {\displaystyle{\displaystyle\xi>0}}
    xml-id
    C14.S5.XMD1.m1gdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4739&oldid=31362"