DLMF:10.32.E17 (Q3537): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1apdec

Revision as of 13:45, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.32.E17
No description defined

    Statements

    Defining formula
    K μ ⁡ ( z ) ⁢ K ν ⁡ ( z ) = 2 ⁢ ∫ 0 ∞ K μ ± ν ⁡ ( 2 ⁢ z ⁢ cosh ⁡ t ) ⁢ cosh ⁡ ( ( μ ∓ ν ) ⁢ t ) ⁢ d t , modified-Bessel-second-kind 𝜇 𝑧 modified-Bessel-second-kind 𝜈 𝑧 2 superscript subscript 0 modified-Bessel-second-kind plus-or-minus 𝜇 𝜈 2 𝑧 𝑡 minus-or-plus 𝜇 𝜈 𝑡 𝑡 {\displaystyle{\displaystyle K_{\mu}\left(z\right)K_{\nu}\left(z\right)=2\int_% {0}^{\infty}K_{\mu\pm\nu}\left(2z\cosh t\right)\cosh\left((\mu\mp\nu)t\right)% \mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:10.32.E17
    0 references
    constraint
    | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}
    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.m2andec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1apdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3537&oldid=39698"