Fungrim symbol: MeromorphicDerivative

Symbol: MeromorphicDerivative —

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

— Complex derivative, allowing poles

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

This operator is equivalent to ComplexDerivative except that whereas ComplexDerivative is undefined at a pole, MeromorphicDerivative gives UnsignedInfinity (

{\tilde \infty}

) at a pole.

Definitions:

Fungrim symbol	Notation	Short description
`MeromorphicDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative, allowing poles
`Derivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Derivative
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative
`UnsignedInfinity`	${\tilde \infty}$	Unsigned infinity

Source code for this entry:

Entry(ID("4c6780"),
    SymbolDefinition(MeromorphicDerivative, MeromorphicDerivative(Call(f, z), For(z, z)), "Complex derivative, allowing poles"),
    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 at a pole,", SourceForm(MeromorphicDerivative), "gives", SourceForm(UnsignedInfinity), "(", UnsignedInfinity, ")", "at a pole."))

Topics using this symbol

The symbol MeromorphicDerivative appears in 3 topics:

Differential equations for Jacobi theta functions (in 12 entries)
Operators (in 2 entries)
Jacobi theta functions (in 1 entries)

Entries using this symbol

The symbol MeromorphicDerivative appears in 14 entries: