DLMF:14.5.E26 (Q4738)

From DRMF
Revision as of 01:25, 2 January 2020 by Admin (talk | contribs) (β€ŽChanged an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:14.5.E26
No description defined

    Statements

    Defining formula
    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),}}
    0 references
    DLMF id
    DLMF:14.5.E26
    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.m2aodec
    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.m1aedec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4738&oldid=31310"