DLMF:36.13.E8
type: Item
Digital Library of Mathematical Functions ID: 36.13.E8
DLMF defining formula: <math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle z(\rho,\phi)=2\pi\left(\rho^{-1/3}u(\phi)\cos% \left(\rho\widetilde{f}(\phi)\right)\mathrm{Ai}\left(-\rho^{2/3}\Delta(\phi)% \right)\*(1+O\left(1/\rho\right))+\rho^{-2/3}v(\phi)\sin\left(\rho\widetilde{f% }(\phi)\right)\mathrm{Ai}'\left(-\rho^{2/3}\Delta(\phi)\right)\*(1+O\left(1/% \rho\right))\right),}}" display="inline"> z ⁢ ( ρ , ϕ ) = 2 ⁢ π ⁢ ( ρ - 1 / 3 ⁢ u ⁢ ( ϕ ) ⁢ cos ⁡ ( ρ ⁢ f ~ ⁢ ( ϕ ) ) ⁢ Ai ⁡ ( - ρ 2 / 3 ⁢ Δ ⁢ ( ϕ ) ) ⁢ ( 1 + O ⁡ ( 1 / ρ ) ) + ρ - 2 / 3 ⁢ v ⁢ ( ϕ ) ⁢ sin ⁡ ( ρ ⁢ f ~ ⁢ ( ϕ ) ) ⁢ Ai ′ ⁡ ( - ρ 2 / 3 ⁢ Δ ⁢ ( ϕ ) ) ⁢ ( 1 + O ⁡ ( 1 / ρ ) ) ) , <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b"> <apply id="p1.1.m1.1.42.2.cmml" xref="p1.1.m1.1.42"> <eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/> <apply id="p1.1.m1.1.42.2.1.cmml" xref="p1.1.m1.1.42.2.1"> <times id="p1.1.m1.1.42.2.1.1.cmml" xref="p1.1.m1.1.42.2.1.1"/> <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑧</ci> <interval closure="open" id="p1.1.m1.1.42.2.1.2.1.cmml" xref="p1.1.m1.1.42.2.1.2"> <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝜌</ci> <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">italic-ϕ</ci> </interval> </apply> <apply id="p1.1.m1.1.42.2.2.cmml" xref="p1.1.m1.1.42.2.2"> <times id="p1.1.m1.1.42.2.2.1.cmml" xref="p1.1.m1.1.42.2.2.1"/> <cn type="integer" id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8">2</cn> <ci id="p1.1.m1.1.9.cmml" xref="p1.1.m1.1.9">𝜋</ci> <apply id="p1.1.m1.1.42.2.2.2.2.cmml" xref="p1.1.m1.1.42.2.2.2"> <plus id="p1.1.m1.1.25.cmml" xref="p1.1.m1.1.25"/> <apply id="p1.1.m1.1.42.2.2.2.2.1.cmml" xref="p1.1.m1.1.42.2.2.2.2.1"> <times id="p1.1.m1.1.19.cmml" xref="p1.1.m1.1.19"/> <apply id="p1.1.m1.1.42.2.2.2.2.1.1.cmml" xref="p1.1.m1.1.42.2.2.2.2.1.1"> <csymbol cd="ambiguous" id="p1.1.m1.1.42.2.2.2.2.1.1.1.cmml" xref="p1.1.m1.1.42.2.2.2.2.1.1">superscript</csymbol> <ci id="p1.1.m1.1.11.cmml" xref="p1.1.m1.1.11">𝜌</ci> <apply id="p1.1.m1.1.12.1.cmml" xr…
constraint: ρ → ∞ <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b"> <apply id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"> <ci id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2">→</ci> <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝜌</ci> <infinity id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/> </apply> </annotation-xml> {\displaystyle{\displaystyle\rho\to\infty}}
Symbols used: Q10893
Symbols used: order not exceeding
Symbols used: the ratio of the circumference of a circle to its diameter
Symbols used: cosine function
Symbols used: Q10751
Symbols used: sine function
Symbols used: real parameter
Symbols used: function
instance of: Digital Library of Mathematical Functions Formula
MaRDI profile type: MaRDI formula profile