Symbol:

`ComplexZeroMultiplicity`— $\mathop{\operatorname{ord}}\limits_{z} f\!\left(z\right)$ — Multiplicity (order) of complex zero`ComplexZeroMultiplicity(f(z), z, c)`, rendered $\mathop{\operatorname{ord}}\limits_{z=c} f\!\left(z\right)$, gives the root multiplicity (order of vanishing) of $f\!\left(z\right)$ at the point $z = c$.

If $f\!\left(c\right) \ne 0$, the multiplicity is zero.

It is required that $f\!\left(z\right)$
is holomorphic and not identically zero in a neighborhood of $c$.

Definitions:

Fungrim symbol | Notation | Short description |
---|---|---|

ComplexZeroMultiplicity | $\mathop{\operatorname{ord}}\limits_{z} f\!\left(z\right)$ | Multiplicity (order) of complex zero |

Source code for this entry:

Entry(ID("231a99"), SymbolDefinition(ComplexZeroMultiplicity, ComplexZeroMultiplicity(f(z), z, z), "Multiplicity (order) of complex zero"), Description(SourceForm(ComplexZeroMultiplicity(f(z), z, c)), ", rendered", ComplexZeroMultiplicity(f(z), z, c), ", gives the root multiplicity (order of vanishing) of", f(z), "at the point", Equal(z, c), "."), Description("If", Unequal(f(c), 0), ", the multiplicity is zero."), Description("It is required that", f(z), "is holomorphic and not identically zero in a neighborhood of", c, "."))