DLMF:10.38.E1 (Q3560): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: psi (or digamma) function / rank
 
Normal rank
Property / Symbols used: psi (or digamma) function / qualifier
 
Defining formula:

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

\digamma@{\NVar{z}}
Property / Symbols used: psi (or digamma) function / qualifier
 
xml-id: C5.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

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

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
Property / Symbols used
 
Property / Symbols used: modified Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: modified Bessel function of the first kind / qualifier
 
Defining formula:

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

\modBesselI{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Bessel function of the first kind / qualifier
 
xml-id: C10.S25.E2.m2adec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

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

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
 
Defining formula:

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

\pderiv{\NVar{f}}{\NVar{x}}
Property / Symbols used: partial derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S5.E3.m4adec
Property / Symbols used
 
Property / Symbols used: partial differential of $$x$$ / rank
 
Normal rank
Property / Symbols used: partial differential of $$x$$ / qualifier
 
Defining formula:

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

\pdiff{\NVar{x}}
Property / Symbols used: partial differential of $$x$$ / qualifier
 
xml-id: C1.S5.E3.m2adec
Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
Defining formula:

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

k
Property / Symbols used: Q11428 / qualifier
 
xml-id: C10.S1.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
Defining formula:

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

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
Defining formula:

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

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1dec

Latest revision as of 12:49, 2 January 2020

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DLMF:10.38.E1
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\modBesselI{\pm\nu}@{z}}{\nu}=\pm\modBesselI{\pm\nu}@{z}\ln@{\tfrac{1}{2}z}\mp(\tfrac{1}{2}z)^{\pm\nu}\sum_{k=0}^{\infty}\frac{\digamma@{k+1\pm\nu}}{\EulerGamma@{k+1\pm\nu}}\frac{(\frac{1}{4}z^{2})^{k}}{k!},}
    0 references
    DLMF id
    DLMF:10.38.E1
    0 references
    Symbols used
    gamma function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\NVar{z}}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    psi (or digamma) function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{\NVar{z}}}
    xml-id
    C5.S2.E2.m2adec
    0 references
    Q10755
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle !}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    modified Bessel function of the first kind
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\NVar{\nu}}@{\NVar{z}}}
    xml-id
    C10.S25.E2.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
    partial derivative of $$f$$ with respect to $$x$$
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\NVar{f}}{\NVar{x}}}
    xml-id
    C1.S5.E3.m4adec
    0 references
    partial differential of $$x$$
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pdiff{\NVar{x}}}
    xml-id
    C1.S5.E3.m2adec
    0 references
    Q11428
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
    xml-id
    C10.S1.XMD3.m1dec
    0 references
    Q11426
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}
    xml-id
    C10.S1.XMD6.m1dec
    0 references
    Q11427
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu}
    xml-id
    C10.S1.XMD7.m1dec
    0 references
     
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