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Fungrim entry: def37e

CAi ⁣(z)+DBi ⁣(z) is holomorphic on zCC \operatorname{Ai}\!\left(z\right) + D \operatorname{Bi}\!\left(z\right) \text{ is holomorphic on } z \in \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)
TeX:
C \operatorname{Ai}\!\left(z\right) + D \operatorname{Bi}\!\left(z\right) \text{ is holomorphic on } z \in \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)
Definitions:
Fungrim symbol Notation Short description
IsHolomorphicf(z) is holomorphic at z=cf(z) \text{ is holomorphic at } z = c Holomorphic predicate
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
Source code for this entry:
Entry(ID("def37e"),
    Formula(IsHolomorphic(Add(Mul(C, AiryAi(z)), Mul(D, AiryBi(z))), ForElement(z, CC))),
    Variables(C, D),
    Assumptions(And(Element(C, CC), Element(D, CC), Not(And(Equal(C, 0), Equal(D, 0))))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-10-05 13:11:19.856591 UTC