DLMF:14.20.E13 (Q4934)

From DRMF
Revision as of 13:34, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:14.20.E13
No description defined

    Statements

    Defining formula
    P - 1 2 + i ⁢ τ ⁡ ( x ) = cosh ⁡ ( τ ⁢ π ) π ⁢ ∫ 1 ∞ P - 1 2 + i ⁢ τ ⁡ ( t ) x + t ⁢ d t , shorthand-Legendre-P-first-kind 1 2 𝑖 𝜏 𝑥 𝜏 𝜋 𝜋 superscript subscript 1 shorthand-Legendre-P-first-kind 1 2 𝑖 𝜏 𝑡 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle P_{-\frac{1}{2}+i\tau}\left(x\right)=\frac{\cosh% \left(\tau\pi\right)}{\pi}\int_{1}^{\infty}\frac{P_{-\frac{1}{2}+i\tau}\left(t% \right)}{x+t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:14.20.E13
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4934&oldid=37871"