DLMF:18.15.E22 (Q5717): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(10 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11333 / rank
 
Normal rank
Property / Symbols used: Q11333 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LaguerrepolyL[\NVar{\alpha}]{\NVar{n}}@{\NVar{x}}}

\LaguerrepolyL[\NVar{\alpha}]{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11333 / qualifier
 
xml-id: C18.S3.T1.t1.r12.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asympexp}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11adec
Property / Symbols used
 
Property / Symbols used: Q11082 / rank
 
Normal rank
Property / Symbols used: Q11082 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \envAiryAi@{\NVar{x}}}

\envAiryAi@{\NVar{x}}
Property / Symbols used: Q11082 / qualifier
 
xml-id: C2.S8.SS3.p4.m4adec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11730 / rank
 
Normal rank
Property / Symbols used: Q11730 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m}

m
Property / Symbols used: Q11730 / qualifier
 
xml-id: C18.S1.XMD5.m1ndec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1mdec
Property / Symbols used
 
Property / Symbols used: DLMF:18.15.E17 / rank
 
Normal rank
Property / Symbols used: DLMF:18.15.E17 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu}

\nu
Property / Symbols used: DLMF:18.15.E17 / qualifier
 
xml-id: C18.S15.XMD14.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11758 / rank
 
Normal rank
Property / Symbols used: Q11758 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta}

\zeta
Property / Symbols used: Q11758 / qualifier
 
xml-id: C18.S15.XMD18.m1adec
Property / Symbols used
 
Property / Symbols used: Q11759 / rank
 
Normal rank
Property / Symbols used: Q11759 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle E_{m}}

E_{m}
Property / Symbols used: Q11759 / qualifier
 
xml-id: C18.S15.XMD19.m1dec
Property / Symbols used
 
Property / Symbols used: coefficient (locally) / rank
 
Normal rank
Property / Symbols used: coefficient (locally) / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle F_{m}}

F_{m}
Property / Symbols used: coefficient (locally) / qualifier
 
xml-id: C18.S15.XMD20.m1dec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1gdec

Latest revision as of 15:40, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.15.E22
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LaguerrepolyL[\alpha]{n}@{\nu x}=(-1)^{n}\frac{e^{\frac{1}{2}\nu x}}{2^{\alpha-\frac{1}{2}}x^{\frac{1}{2}\alpha+\frac{1}{4}}}\*\left(\frac{\zeta}{x-1}\right)^{\frac{1}{4}}\left(\frac{\AiryAi@{\nu^{\frac{2}{3}}\zeta}}{\nu^{\frac{1}{3}}}\sum_{m=0}^{M-1}\frac{E_{m}(\zeta)}{\nu^{2m}}+\frac{\AiryAi'@{\nu^{\frac{2}{3}}\zeta}}{\nu^{\frac{5}{3}}}\sum_{m=0}^{M-1}\frac{F_{m}(\zeta)}{\nu^{2m}}+\envAiryAi@{\nu^{\frac{2}{3}}\zeta}\bigO@{\frac{1}{\nu^{2M-\frac{2}{3}}}}\right),}
    0 references
    DLMF id
    DLMF:18.15.E22
    0 references
    Symbols used
    Q10919
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryAi@{\NVar{z}}}
    xml-id
    C9.S2.SS1.m1adec
    0 references
    order not exceeding
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \bigO@{\NVar{x}}}
    xml-id
    C2.S1.E3.m2afdec
    0 references
    Q11333
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \LaguerrepolyL[\NVar{\alpha}]{\NVar{n}}@{\NVar{x}}}
    xml-id
    C18.S3.T1.t1.r12.m2abdec
    0 references
    Q10931
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \asympexp}
    xml-id
    C2.S1.SS3.p1.m11adec
    0 references
    Q11082
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \envAiryAi@{\NVar{x}}}
    xml-id
    C2.S8.SS3.p4.m4adec
    0 references
    base of natural logarithm
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    Q11730
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m}
    xml-id
    C18.S1.XMD5.m1ndec
    0 references
    Q11726
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}
    xml-id
    C18.S1.XMD6.m1mdec
    0 references
    DLMF:18.15.E17
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu}
    xml-id
    C18.S15.XMD14.m1bdec
    0 references
    Q11758
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta}
    xml-id
    C18.S15.XMD18.m1adec
    0 references
    Q11759
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle E_{m}}
    xml-id
    C18.S15.XMD19.m1dec
    0 references
    coefficient (locally)
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle F_{m}}
    xml-id
    C18.S15.XMD20.m1dec
    0 references
    Q11727
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}
    xml-id
    C18.S2.XMD3.m1gdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5717&oldid=59805"