DLMF:13.18.E9 (Q4578): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: modified Bessel function of the second kind / rank
 
Normal rank
Property / Symbols used: modified Bessel function of the second kind / qualifier
 
Defining formula:

K ν ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modBesselK{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Bessel function of the second kind / qualifier
 
xml-id: C10.S25.E3.m2adec
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1hdec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2abdec

Latest revision as of 16:13, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:13.18.E9
No description defined

    Statements

    W 0 , ν ( 2 z ) = 2 z / π K ν ( z ) , Whittaker-confluent-hypergeometric-W 0 𝜈 2 𝑧 2 𝑧 𝜋 modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle W_{0,\nu}\left(2z\right)=\sqrt{\ifrac{2z}{\pi}}K_% {\nu}\left(z\right),}}
    0 references
    DLMF:13.18.E9
    0 references
    W κ , μ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    C13.S14.E3.m2acdec
    0 references
    K ν ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S25.E3.m2adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C13.S1.XMD6.m1hdec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2abdec
    0 references