DLMF:9.7.E13 (Q2820): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
Defining formula:

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

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1ahdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

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

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2addec
Property / Symbols used
 
Property / Symbols used: Q11385 / rank
 
Normal rank
Property / Symbols used: Q11385 / qualifier
 
Defining formula:

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

k
Property / Symbols used: Q11385 / qualifier
 
xml-id: C9.S1.XMD1.m1idec
Property / Symbols used
 
Property / Symbols used: Q11381 / rank
 
Normal rank
Property / Symbols used: Q11381 / qualifier
 
Defining formula:

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

z
Property / Symbols used: Q11381 / qualifier
 
xml-id: C9.S1.XMD3.m1idec
Property / Symbols used
 
Property / Symbols used: Q11386 / rank
 
Normal rank
Property / Symbols used: Q11386 / qualifier
 
Defining formula:

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

\delta
Property / Symbols used: Q11386 / qualifier
 
xml-id: C9.S1.XMD4.m1hdec
Property / Symbols used
 
Property / Symbols used: change of variable (locally) / rank
 
Normal rank
Property / Symbols used: change of variable (locally) / qualifier
 
Defining formula:

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

\zeta
Property / Symbols used: change of variable (locally) / qualifier
 
xml-id: C9.S7.XMD1.m1idec
Property / Symbols used
 
Property / Symbols used: Q11387 / rank
 
Normal rank
Property / Symbols used: Q11387 / qualifier
 
Defining formula:

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

u_{s}
Property / Symbols used: Q11387 / qualifier
 
xml-id: C9.S7.XMD2.m1edec

Latest revision as of 13:35, 2 January 2020

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DLMF:9.7.E13
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{ze^{\pm\pi i/3}}\mathrel{\asympexp}\sqrt{\frac{2}{\pi}}\frac{e^{\pm\pi i/6}}{z^{1/4}}\*\left(\cos@{\zeta-\tfrac{1}{4}\pi\mp\tfrac{1}{2}\iunit\ln@@{2}}\sum_{k=0}^{\infty}(-1)^{k}\frac{u_{2k}}{\zeta^{2k}}+\sin@{\zeta-\tfrac{1}{4}\pi\mp\tfrac{1}{2}\iunit\ln@@{2}}\sum_{k=0}^{\infty}(-1)^{k}\frac{u_{2k+1}}{\zeta^{2k+1}}\right),}
    0 references
    DLMF id
    DLMF:9.7.E13
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\phase@@{z}|\leq\tfrac{2}{3}\pi-\delta}
    0 references
    Symbols used
    Q11081
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \AiryBi@{\NVar{z}}}
    xml-id
    C9.S2.SS1.m2addec
    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.m11ahdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}
    xml-id
    C3.S12.E1.m2ajdec
    0 references
    cosine function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\NVar{z}}}
    xml-id
    C4.S14.E2.m2addec
    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.m2addec
    0 references
    imaginary unit
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}
    xml-id
    C1.S9.E1.m2adec
    0 references
    principal branch of logarithm function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q10817
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase}
    xml-id
    C1.S9.E7.m1ahdec
    0 references
    sine function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\NVar{z}}}
    xml-id
    C4.S14.E1.m2addec
    0 references
    Q11385
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
    xml-id
    C9.S1.XMD1.m1idec
    0 references
    Q11381
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}
    xml-id
    C9.S1.XMD3.m1idec
    0 references
    Q11386
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \delta}
    xml-id
    C9.S1.XMD4.m1hdec
    0 references
    change of variable (locally)
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta}
    xml-id
    C9.S7.XMD1.m1idec
    0 references
    Q11387
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u_{s}}
    xml-id
    C9.S7.XMD2.m1edec
    0 references
     
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