Fungrim entry: 0895b1

Symbol: IsMeromorphic —

f(z) \text{ is meromorphic at } z = c

— Meromorphic predicate

IsMeromorphic(f(z), For(z, c)), rendered

f(z) \text{ is meromorphic at } z = c

, represents the predicate that

f(z)

is meromorphic in some open neighborhood of the point

c

IsMeromorphic(f(z), ForElement(z, S)), rendered

f(z) \text{ is meromorphic on } z \in S

, represents the predicate that

f(z)

is meromorphic in some open neighborhood of every point in the set

S

As a special case

f(z) \text{ is meromorphic at } z = {\tilde \infty}

is equivalent to

f\!\left(\frac{1}{z}\right) \text{ is meromorphic at } z = 0

As a special case

f(z) \text{ is meromorphic at } z = i \infty

represents the predicate that

f(z)

is a periodic function on the upper half plane that is meromorphic at infinity (in the sense of modular function theory)

Definitions:

Fungrim symbol	Notation	Short description
`IsMeromorphic`	$f(z) \text{ is meromorphic at } z = c$	Meromorphic predicate
`UnsignedInfinity`	${\tilde \infty}$	Unsigned infinity
`ConstI`	$i$	Imaginary unit
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("0895b1"),
    SymbolDefinition(IsMeromorphic, IsMeromorphic(f(z), For(z, c)), "Meromorphic predicate"),
    Description(SourceForm(IsMeromorphic(f(z), For(z, c))), ", rendered", IsMeromorphic(f(z), For(z, c)), ", represents the predicate", "that", f(z), "is meromorphic in some open neighborhood of the point", c, "."),
    Description(SourceForm(IsMeromorphic(f(z), ForElement(z, S))), ", rendered", IsMeromorphic(f(z), ForElement(z, S)), ", represents the predicate", "that", f(z), "is meromorphic in some open neighborhood of every point in the set", S, "."),
    Description("As a special case", IsMeromorphic(f(z), For(z, UnsignedInfinity)), " is equivalent to", IsMeromorphic(f(Div(1, z)), For(z, 0)), "."),
    Description("As a special case", IsMeromorphic(f(z), For(z, Mul(ConstI, Infinity))), " represents the predicate that", f(z), "is a periodic function on the upper half plane that is meromorphic at infinity (in the sense of modular function theory)"))

Topics using this entry

Operators