Fungrim symbol: ComplexBranchDerivative

Symbol: ComplexBranchDerivative —

\frac{d}{d z}\, f\!\left(z\right)

— Complex derivative, allowing branch cuts

The call syntax for this operator is the same as for Derivative.

This operator is equivalent to ComplexDerivative except that whereas ComplexDerivative is undefined on a branch cut (where the function is not complex differentiable), ComplexBranchDerivative gives the complex derivative of the analytically continued function across the branch cut.

Definitions:

Fungrim symbol	Notation	Short description
`ComplexBranchDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative, allowing branch cuts
`Derivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Derivative
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative

Source code for this entry:

Entry(ID("96f695"),
    SymbolDefinition(ComplexBranchDerivative, ComplexBranchDerivative(Call(f, z), For(z, z)), "Complex derivative, allowing branch cuts"),
    Description("The call syntax for this operator is the same as for", SourceForm(Derivative), "."),
    Description("This operator is equivalent to", SourceForm(ComplexDerivative), "except that whereas", SourceForm(ComplexDerivative), "is undefined on a branch cut (where the function is not complex differentiable),", SourceForm(ComplexBranchDerivative), "gives the complex derivative of the analytically continued function across the branch cut."))

Topics using this symbol

The symbol ComplexBranchDerivative appears in 4 topics:

Series and product representations of Jacobi theta functions (in 2 entries)
Operators (in 2 entries)
Digamma function (in 2 entries)
Barnes G-function (in 1 entries)

Entries using this symbol

The symbol ComplexBranchDerivative appears in 7 entries: