DLMF:14.15.E16 (Q4862): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(2 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11617 / rank
 
Normal rank
Property / Symbols used: Q11617 / qualifier
 
Defining formula:

β 𝛽 {\displaystyle{\displaystyle\beta}}

\beta
Property / Symbols used: Q11617 / qualifier
 
xml-id: C14.S15.XMD10.m1adec
Property / Symbols used
 
Property / Symbols used: Q11618 / rank
 
Normal rank
Property / Symbols used: Q11618 / qualifier
 
Defining formula:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11618 / qualifier
 
xml-id: C14.S15.XMD11.m1adec
Property / Symbols used
 
Property / Symbols used: Q11619 / rank
 
Normal rank
Property / Symbols used: Q11619 / qualifier
 
Defining formula:

α 𝛼 {\displaystyle{\displaystyle\alpha}}

\alpha
Property / Symbols used: Q11619 / qualifier
 
xml-id: C14.S15.XMD9.m1adec

Latest revision as of 01:51, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:14.15.E16
No description defined

    Statements

    Defining formula
    𝖰 ν - μ ⁡ ( x ) = - π ⁢ β 2 ⁢ ( y - α 2 1 - α 2 - x 2 ) 1 / 4 ⁢ ( Y μ ⁡ ( ( ν + 1 2 ) ⁢ y 1 / 2 ) + O ⁡ ( 1 ν ) ⁢ env ⁢ Y μ ⁡ ( ( ν + 1 2 ) ⁢ y 1 / 2 ) ) , Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 𝜋 𝛽 2 superscript 𝑦 superscript 𝛼 2 1 superscript 𝛼 2 superscript 𝑥 2 1 4 Bessel-Y-Weber 𝜇 𝜈 1 2 superscript 𝑦 1 2 Big-O 1 𝜈 envelope-Bessel-Y 𝜇 𝜈 1 2 superscript 𝑦 1 2 {\displaystyle{\displaystyle\mathsf{Q}^{-\mu}_{\nu}\left(x\right)=-\frac{\pi% \beta}{2}\left(\frac{y-\alpha^{2}}{1-\alpha^{2}-x^{2}}\right)^{1/4}\left(Y_{% \mu}\left(\left(\nu+\tfrac{1}{2}\right)y^{1/2}\right)+O\left(\frac{1}{\nu}% \right)\mathrm{env}\mskip-2.0mu Y_{\mu}\left(\left(\nu+\tfrac{1}{2}\right)y^{1% /2}\right)\right),}}
    0 references
    DLMF id
    DLMF:14.15.E16
    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.m2aadec
    0 references
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2akdec
    0 references
    Ferrers function of the second kind
    Defining formula
    𝖰 ν μ ⁡ ( x ) Ferrers-Legendre-Q-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E2.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    Q11091
    Defining formula
    env ⁢ Y ν ⁡ ( x ) envelope-Bessel-Y 𝜈 𝑥 {\displaystyle{\displaystyle\mathrm{env}\mskip-2.0mu Y_{\NVar{\nu}}\left(\NVar% {x}\right)}}
    xml-id
    C2.S8.SS4.p5.m4aadec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1idec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1ldec
    0 references
    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1ldec
    0 references
    Q11617
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C14.S15.XMD10.m1adec
    0 references
    Q11618
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C14.S15.XMD11.m1adec
    0 references
    Q11619
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C14.S15.XMD9.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4862&oldid=35183"