DLMF:14.12.E13 (Q4834): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3akdec
Property / Symbols used
 
Property / Symbols used: Q11597 / rank
 
Normal rank
Property / Symbols used: Q11597 / qualifier
 
Defining formula:

𝑸 ν ( z ) = 𝑸 ν 0 ( z ) shorthand-associated-Legendre-black-Q 𝜈 𝑧 associated-Legendre-black-Q 0 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}_{\NVar{\nu}}\left(\NVar{z}\right)=% \boldsymbol{Q}^{0}_{\nu}\left(z\right)}}

\assLegendreOlverQ[]{\NVar{\nu}}@{\NVar{z}}=\assLegendreOlverQ[0]{\nu}@{z}
Property / Symbols used: Q11597 / qualifier
 
xml-id: C14.S2.SS2.p2.m6adec
Property / Symbols used
 
Property / Symbols used: Q11589 / rank
 
Normal rank
Property / Symbols used: Q11589 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11589 / qualifier
 
xml-id: C14.S1.XMD1.m1jdec
Property / Symbols used
 
Property / Symbols used: Q11602 / rank
 
Normal rank
Property / Symbols used: Q11602 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11602 / qualifier
 
xml-id: C14.S1.XMD6.m1ddec

Latest revision as of 01:45, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:14.12.E13
No description defined

    Statements

    𝑸 n ( x ) = 1 2 ( n ! ) - 1 1 P n ( t ) x - t d t . shorthand-associated-Legendre-black-Q 𝑛 𝑥 1 2 𝑛 superscript subscript 1 1 Legendre-spherical-polynomial 𝑛 𝑡 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle\boldsymbol{Q}_{n}\left(x\right)=\frac{1}{2(n!)}% \int_{-1}^{1}\frac{P_{n}\left(t\right)}{x-t}\mathrm{d}t.}}
    0 references
    DLMF:14.12.E13
    0 references
    P n ( x ) Legendre-spherical-polynomial 𝑛 𝑥 {\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
    C18.S3.T1.t1.r10.m2aadec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1akdec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5addec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3akdec
    0 references
    𝑸 ν ( z ) = 𝑸 ν 0 ( z ) shorthand-associated-Legendre-black-Q 𝜈 𝑧 associated-Legendre-black-Q 0 𝜈 𝑧 {\displaystyle{\displaystyle\boldsymbol{Q}_{\NVar{\nu}}\left(\NVar{z}\right)=% \boldsymbol{Q}^{0}_{\nu}\left(z\right)}}
    C14.S2.SS2.p2.m6adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C14.S1.XMD1.m1jdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C14.S1.XMD6.m1ddec
    0 references