Fungrim entry: 1f0577

$\mathop{\operatorname{poles}\,}\limits_{z \in \mathbb{C} \cup \left\{{\tilde \infty}\right\}} \left[C \operatorname{Ai}\!\left(z\right) + D \operatorname{Bi}\!\left(z\right)\right] = \left\{\right\}$
Assumptions:$C \in \mathbb{C} \;\mathbin{\operatorname{and}}\; D \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{not} \left(C = 0 \;\mathbin{\operatorname{and}}\; D = 0\right)$
TeX:
\mathop{\operatorname{poles}\,}\limits_{z \in \mathbb{C} \cup \left\{{\tilde \infty}\right\}} \left[C \operatorname{Ai}\!\left(z\right) + D \operatorname{Bi}\!\left(z\right)\right] = \left\{\right\}

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
AiryAi$\operatorname{Ai}\!\left(z\right)$ Airy function of the first kind
AiryBi$\operatorname{Bi}\!\left(z\right)$ Airy function of the second kind
CC$\mathbb{C}$ Complex numbers
UnsignedInfinity${\tilde \infty}$ Unsigned infinity
Source code for this entry:
Entry(ID("1f0577"),
Formula(Equal(Poles(Add(Mul(C, AiryAi(z)), Mul(D, AiryBi(z))), ForElement(z, Union(CC, Set(UnsignedInfinity)))), Set())),
Variables(C, D),
Assumptions(And(Element(C, CC), Element(D, CC), Not(And(Equal(C, 0), Equal(D, 0))))))

Topics using this entry

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

2021-03-15 19:12:00.328586 UTC