DLMF:4.38.E10 (Q1960): Difference between revisions

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Property / constraint
 

z 0 greater-than-or-less-than 𝑧 0 {\displaystyle{\displaystyle\Re z\gtrless 0}}

\realpart@@{z}\gtrless 0
Property / constraint: z 0 greater-than-or-less-than 𝑧 0 {\displaystyle{\displaystyle\Re z\gtrless 0}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
 
Normal rank
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
Defining formula:

d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

\deriv{\NVar{f}}{\NVar{x}}
Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
 
xml-id: C1.S4.E4.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11246 / rank
 
Normal rank
Property / Symbols used: Q11246 / qualifier
 
Defining formula:

arccosh z hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}

\acosh@@{\NVar{z}}
Property / Symbols used: Q11246 / qualifier
 
xml-id: C4.S37.SS2.p1.m9abdec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1acdec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1hdec

Latest revision as of 19:19, 1 January 2020

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DLMF:4.38.E10
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    Statements

    d d z arccosh z = ± ( z 2 - 1 ) - 1 / 2 , derivative 𝑧 hyperbolic-inverse-cosine 𝑧 plus-or-minus superscript superscript 𝑧 2 1 1 2 {\displaystyle{\displaystyle\frac{\mathrm{d}}{\mathrm{d}z}\operatorname{% arccosh}z=\pm(z^{2}-1)^{-1/2},}}
    0 references
    DLMF:4.38.E10
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    z 0 greater-than-or-less-than 𝑧 0 {\displaystyle{\displaystyle\Re z\gtrless 0}}
    0 references
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2aadec
    0 references
    arccosh z hyperbolic-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{arccosh}\NVar{z}}}
    C4.S37.SS2.p1.m9abdec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1acdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C4.S1.XMD8.m1hdec
    0 references