DLMF:36.12.E3
type: Item
Digital Library of Mathematical Functions ID: 36.12.E3
DLMF defining formula: <math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle I(\mathbf{y},k)=\frac{\exp\left(ikA(\mathbf{y})% \right)}{k^{1/(K+2)}}\sum\limits_{m=0}^{K}\frac{a_{m}(\mathbf{y})}{k^{m/(K+2)}% }\left(\delta_{m,0}-\left(1-\delta_{m,0}\right)i\frac{\partial}{\partial z_{m}% }\right)\Psi_{K}\left(\mathbf{z}(\mathbf{y};k)\right)\left(1+O\left(\frac{1}{k% }\right)\right),}}" display="inline"> I ⁢ ( 𝐲 , k ) = exp ⁡ ( i ⁢ k ⁢ A ⁢ ( 𝐲 ) ) k 1 / ( K + 2 ) ⁢ <munderover id="p1.1.m1.1.31.2.2.2.1a" xref="p1.1.m1.1.31.2.2.2.1.cmml"> ∑ m = 0 K </munderover> a m ⁢ ( 𝐲 ) k m / ( K + 2 ) ⁢ ( δ m , 0 - ( 1 - δ m , 0 ) ⁢ i ⁢ ∂ ∂ ⁡ z m ) ⁢ Ψ K ⁡ ( 𝐳 ⁢ ( 𝐲 ; k ) ) ⁢ ( 1 + O ⁡ ( 1 k ) ) , <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b"> <apply id="p1.1.m1.1.31.2.cmml" xref="p1.1.m1.1.31"> <eq id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"/> <apply id="p1.1.m1.1.31.2.1.cmml" xref="p1.1.m1.1.31.2.1"> <times id="p1.1.m1.1.31.2.1.1.cmml" xref="p1.1.m1.1.31.2.1.1"/> <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝐼</ci> <interval closure="open" id="p1.1.m1.1.31.2.1.2.1.cmml" xref="p1.1.m1.1.31.2.1.2"> <ci id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">𝐲</ci> <ci id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5">𝑘</ci> </interval> </apply> <apply id="p1.1.m1.1.31.2.2.cmml" xref="p1.1.m1.1.31.2.2"> <times id="p1.1.m1.1.31.2.2.1.cmml" xref="p1.1.m1.1.31.2.2.1"/> <apply id="p1.1.m1.1.8.cmml" xref="p1.1.m1.1.8"> <divide id="p1.1.m1.1.8.1.cmml" xref="p1.1.m1.1.8"/> <apply id="p1.1.m1.1.8.2.1.1.cmml" xref="p1.1.m1.1.8.2.1.7.2"> <exp id="p1.1.m1.1.8.2.1.2.1.1.cmml" xref="p1.1.m1.1.8.2.1.2.1.2"/> <apply id="p1.1.m1.1.8.2.1.5.cmml" xref="p1.1.m1.1.8.2.1.5"> <times id="p1.1.m1.1.8.2.1.5.7.cmml" xref="p1.1.m1.1.8.2.1.5.7"/> <ci id="p1.1.m1.1.8.2.1.5.1.cmml" xref="p1.1.m1.1.8.2.1.5.1">𝑖</ci> <ci id="p1.1.m1.1.8.2.1.5.2.cmml" xref="p1.1.m1.1.8.2.1.5.2">𝑘</ci> <ci id="p1.1.m1.1.8.2.1.5.3.cmml" xref="p1.1.m1.1.8.2.1.5.3">𝐴</ci> <ci id="p1.1.m1.1.8.2.1.5.5.cmml" xref="…
Symbols used: order not exceeding
Symbols used: Q10742
Symbols used: canonical integral function
Symbols used: exponential function
Symbols used: imaginary unit
Symbols used: partial derivative of $$f$$ with respect to $$x$$
Symbols used: partial differential of $$x$$
Symbols used: integer
Symbols used: variable
Symbols used: codimension
Symbols used: oscillatory integral (locally)
Symbols used: function (locally)
Symbols used: function
instance of: Digital Library of Mathematical Functions Formula
MaRDI profile type: MaRDI formula profile