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Fungrim entry: def37e

HolomorphicDomain ⁣(CAi ⁣(z)+DBi ⁣(z),z,C{~})=C\operatorname{HolomorphicDomain}\!\left(C \operatorname{Ai}\!\left(z\right) + D \operatorname{Bi}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \mathbb{C}
Assumptions:CCandDCandnot(C=0andD=0)C \in \mathbb{C} \,\mathbin{\operatorname{and}}\, D \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{not} \left(C = 0 \,\mathbin{\operatorname{and}}\, D = 0\right)
\operatorname{HolomorphicDomain}\!\left(C \operatorname{Ai}\!\left(z\right) + D \operatorname{Bi}\!\left(z\right), z, \mathbb{C} \cup \left\{{\tilde \infty}\right\}\right) = \mathbb{C}

C \in \mathbb{C} \,\mathbin{\operatorname{and}}\, D \in \mathbb{C} \,\mathbin{\operatorname{and}}\,  \operatorname{not} \left(C = 0 \,\mathbin{\operatorname{and}}\, D = 0\right)
Fungrim symbol Notation Short description
AiryAiAi ⁣(z)\operatorname{Ai}\!\left(z\right) Airy function of the first kind
AiryBiBi ⁣(z)\operatorname{Bi}\!\left(z\right) Airy function of the second kind
CCC\mathbb{C} Complex numbers
UnsignedInfinity~{\tilde \infty} Unsigned infinity
Source code for this entry:
    Formula(Equal(HolomorphicDomain(Add(Mul(C, AiryAi(z)), Mul(D, AiryBi(z))), z, Union(CC, Set(UnsignedInfinity))), CC)),
    Variables(C, D),
    Assumptions(And(Element(C, CC), Element(D, CC), Not(And(Equal(C, 0), Equal(D, 0))))))

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2019-08-21 11:44:15.926409 UTC