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Fungrim entry: b4b319

Symbol: ComplexDerivative ddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
The call syntax for this operator is the same as for Derivative.
The result is defined as f(z)=limh0f ⁣(z+h)f(z)hf'(z) = \lim_{h \to 0} \frac{f\!\left(z + h\right) - f(z)}{h} where the limit is taken with respect to a complex variable hh ( ComplexLimit ).
If this limit exists (and is finite), then ff is holomorphic at zz.
Definitions:
Fungrim symbol Notation Short description
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
Derivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Derivative
ComplexLimitlimzaf(z)\lim_{z \to a} f(z) Limiting value, complex variable
Source code for this entry:
Entry(ID("b4b319"),
    SymbolDefinition(ComplexDerivative, ComplexDerivative(Call(f, z), For(z, z)), "Complex derivative"),
    Description("The call syntax for this operator is the same as for", SourceForm(Derivative), "."),
    Description("The result is defined as", Equal(ComplexDerivative(f(z), For(z, z)), ComplexLimit(Div(Sub(f(Add(z, h)), f(z)), h), For(h, 0))), "where the limit is taken with respect to a complex variable", h, "(", SourceForm(ComplexLimit), ")."),
    Description("If this limit exists (and is finite), then", f, "is holomorphic at", z, "."))

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2021-03-15 19:12:00.328586 UTC