DLMF:10.15.E9 (Q3155): 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: 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.m2agdec

Revision as of 15:26, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:10.15.E9
No description defined

    Statements

    Defining formula
    ∂ ⁡ Y ν ⁡ ( x ) ∂ ⁡ ν | ν = - 1 2 = - 2 π ⁢ x ⁢ ( Ci ⁡ ( 2 ⁢ x ) ⁢ sin ⁡ x - ( Si ⁡ ( 2 ⁢ x ) - π ) ⁢ cos ⁡ x ) . evaluated-at partial-derivative Bessel-Y-Weber 𝜈 𝑥 𝜈 𝜈 1 2 2 𝜋 𝑥 cosine-integral 2 𝑥 𝑥 sine-integral 2 𝑥 𝜋 𝑥 {\displaystyle{\displaystyle\left.\frac{\partial Y_{\nu}\left(x\right)}{% \partial\nu}\right|_{\nu=-\frac{1}{2}}=-\sqrt{\frac{2}{\pi x}}\left(\mathrm{Ci% }\left(2x\right)\sin x-\left(\mathrm{Si}\left(2x\right)-\pi\right)\cos x\right% ).}}
    0 references
    DLMF id
    DLMF:10.15.E9
    0 references
    Symbols used
    Bessel function of the second kind
    Defining formula
    Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E3.m2aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3155&oldid=57760"