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Fungrim entry: 1b6a57

Symbol: Derivative ddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Derivative
Derivative(f(z), For(z, a)), rendered as [ddzf ⁣(z)]z=a\left[ \frac{d}{d z}\, f\!\left(z\right) \right]_{z = a} or f(a)f'(a), represents the derivative of f(z)f(z) evaluated at z=az = a.
Derivative(f(z), For(z, a, n)), rendered as [dndznf ⁣(z)]z=a\left[ \frac{d^{n}}{{d z}^{n}} f\!\left(z\right) \right]_{z = a} or f(n)(a){f}^{(n)}(a), represents the order nn derivative of f(z)f(z) evaluated at z=az = a.
The second argument zz defines a locally bound variable for the expression in the first argument. With the evaluation point set to a=za = z, Derivative(f(z), For(z, z)) may render more simply as ddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right).
This operator is ambiguous since the intended meaning could be a real derivative, a complex derivative, or some other form of derivative. It is better to use RealDerivative, ComplexDerivative, ComplexBranchDerivative, or MeromorphicDerivative.
Definitions:
Fungrim symbol Notation Short description
Derivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Derivative
RealDerivativeddxf ⁣(x)\frac{d}{d x}\, f\!\left(x\right) Real derivative
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
ComplexBranchDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative, allowing branch cuts
MeromorphicDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative, allowing poles
Source code for this entry:
Entry(ID("1b6a57"),
    SymbolDefinition(Derivative, Derivative(Call(f, z), For(z, z)), "Derivative"),
    Description(SourceForm(Derivative(f(z), For(z, a))), ", rendered as ", Derivative(Call(f, z), For(z, a)), "or", Derivative(f(z), For(z, a)), ", represents the derivative of", f(z), "evaluated at", Equal(z, a), "."),
    Description(SourceForm(Derivative(f(z), For(z, a, n))), ", rendered as ", Derivative(Call(f, z), For(z, a, n)), "or", Derivative(f(z), For(z, a, n)), ", represents the order", n, "derivative of", f(z), "evaluated at", Equal(z, a), "."),
    Description("The second argument", z, "defines a locally bound variable for the expression in the first argument. With the evaluation point set to", Equal(a, z), ",", SourceForm(Derivative(f(z), For(z, z))), "may render more simply as", Derivative(Call(f, z), For(z, z)), "."),
    Description("This operator is ambiguous since the intended meaning could be a real derivative, a complex derivative, or some other form of derivative.", "It is better to use", SourceForm(RealDerivative), ",", SourceForm(ComplexDerivative), ",", SourceForm(ComplexBranchDerivative), ", or", SourceForm(MeromorphicDerivative), "."))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-08-27 09:56:25.682319 UTC