DLMF:11.10.E31
type: Item
Digital Library of Mathematical Functions ID: 11.10.E31
DLMF defining formula: <math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle{\mathbf{E}_{\nu}\left(z\right)=}\\ {-2\cos\left(\tfrac{1}{2}\nu\pi\right)\sum_{k=0}^{\infty}(-1)^{k}J_{k-\frac{1}% {2}\nu+\frac{1}{2}}\left(\tfrac{1}{2}z\right)J_{k+\frac{1}{2}\nu+\frac{1}{2}}% \left(\tfrac{1}{2}z\right)}+{2\sin\left(\tfrac{1}{2}\nu\pi\right)\sideset{}{{}% ^{\prime}}{\sum}_{k=0}^{\infty}(-1)^{k}J_{k-\frac{1}{2}\nu}\left(\tfrac{1}{2}z% \right)J_{k+\frac{1}{2}\nu}\left(\tfrac{1}{2}z\right)},}}" display="inline"> 𝐄 ν ⁡ ( z ) = - 2 ⁢ cos ⁡ ( 1 2 ⁢ ν ⁢ π ) ⁢ <munderover id="p1.1.m1.1.32.2.1.1.1.2.1a" xref="p1.1.m1.1.32.2.1.1.1.2.1.cmml"> ∑ k = 0 ∞ </munderover> ( - 1 ) k ⁢ J k - 1 2 ⁢ ν + 1 2 ⁡ ( 1 2 ⁢ z ) ⁢ J k + 1 2 ⁢ ν + 1 2 ⁡ ( 1 2 ⁢ z ) + 2 ⁢ sin ⁡ ( 1 2 ⁢ ν ⁢ π ) ⁢ <munderover id="p1.1.m1.1.32.2.1.2.2" xref="p1.1.m1.1.32.2.1.2.2.cmml"> ∑ ′ k = 0 <mphantom id="p1.1.m1.1.32.2.1.2.2b" xref="p1.1.m1.1.32.2.1.2.2.cmml"> ′ </mphantom> ∞ <mphantom id="p1.1.m1.1.32.2.1.2.2d" xref="p1.1.m1.1.32.2.1.2.2.cmml"> ′ </mphantom> </munderover> ⁢ ( - 1 ) k ⁢ J k - 1 2 ⁢ ν ⁡ ( 1 2 ⁢ z ) ⁢ J k + 1 2 ⁢ ν ⁡ ( 1 2 ⁢ z ) , <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b"> <apply id="p1.1.m1.1.32.2.cmml" xref="p1.1.m1.1.32"> <eq id="p1.1.m1.1.2.cmml" xref="p1.1.m1.1.2"/> <apply id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1.7.2"> <apply id="p1.1.m1.1.1.2.1.1.cmml" xref="p1.1.m1.1.1.2.1.4"> <csymbol cd="dlmf" id="p1.1.m1.1.1.2.1.1.1.cmml" xref="p1.1.m1.1.1.2.1.2">Weber-E</csymbol> <ci id="p1.1.m1.1.1.2.1.3.1.cmml" xref="p1.1.m1.1.1.2.1.3.1">𝜈</ci> </apply> <ci id="p1.1.m1.1.1.5.cmml" xref="p1.1.m1.1.1.5">𝑧</ci> </apply> <apply id="p1.1.m1.1.32.2.1.cmml" xref="p1.1.m1.1.32.2.1"> <plus id="p1.1.m1.1.17.cmml" xref="p1.1.m1.1.17"/> <apply id="p1.1.m1.1.32.2.1.1.cmml" xref="p1.1.m1.1.32.2.1.1"> <minus id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"/> <apply id="p1.1.m1.1.32.2.1.1.1.cmml" xref="p1.1.m1.1.32.2.1.1.1"> <times id="p1.1.m1.1.32.2.1.1.1.1.cmml" xref="p1…
Symbols used: Bessel function of the first kind
Symbols used: Weber function
Symbols used: the ratio of the circumference of a circle to its diameter
Symbols used: cosine function
Symbols used: sine function
Symbols used: complex variable
Symbols used: real or complex order
Symbols used: nonnegative integer
instance of: Digital Library of Mathematical Functions Formula
MaRDI profile type: MaRDI formula profile