Modified Bessel function of the first kind: Differentiation (formula 03.02.20.0007)

BesselI

$Mathematica Notation$

Bessel-Type Functions

BesselI[nu,z]

Differentiation

Low-order differentiation

With respect to z

http://functions.wolfram.com/03.02.20.0007.01

Input Form

D[BesselI[0, z], z] == BesselI[1, z]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["BesselI", "[", RowBox[List["0", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List["BesselI", "[", RowBox[List["1", ",", "z"]], "]"]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> ∂ </mo> <mrow> <msub> <mi> I </mi> <mn> 0 </mn> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <mi> z </mi> </mrow> </mfrac> <mo> ⩵ </mo> <mrow> <msub> <mi> I </mi> <mn> 1 </mn> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 1 </cn> <ci> z </ci> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["BesselI", "[", RowBox[List["0", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["BesselI", "[", RowBox[List["1", ",", "z"]], "]"]]]]]]

Date Added to functions.wolfram.com (modification date)

2001-10-29