2.10.E28
type: Item
Digital Library of Mathematical Functions ID: 2.10.E28
DLMF defining formula: f n - g n = 1 2 ⁢ π ⁢ i ⁢ ∫ | z | = r f ⁢ ( z ) - g ⁢ ( z ) z n + 1 ⁢ d z = 1 2 ⁢ π ⁢ r n ⁢ ∫ 0 2 ⁢ π ( f ⁢ ( r ⁢ e i ⁢ θ ) - g ⁢ ( r ⁢ e i ⁢ θ ) ) ⁢ e - n ⁢ i ⁢ θ ⁢ d θ . <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b"> <apply id="p1.1.m1.1.36.2.cmml" xref="p1.1.m1.1.36"> <and id="p1.1.m1.1.36.2a.cmml" xref="p1.1.m1.1.36"/> <apply id="p1.1.m1.1.36.2b.cmml" xref="p1.1.m1.1.36"> <eq id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6"/> <apply id="p1.1.m1.1.36.2.2.cmml" xref="p1.1.m1.1.36.2.2"> <minus id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/> <apply id="p1.1.m1.1.36.2.2.1.cmml" xref="p1.1.m1.1.36.2.2.1"> <csymbol cd="ambiguous" id="p1.1.m1.1.36.2.2.1.1.cmml" xref="p1.1.m1.1.36.2.2.1">subscript</csymbol> <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑓</ci> <ci id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">𝑛</ci> </apply> <apply id="p1.1.m1.1.36.2.2.2.cmml" xref="p1.1.m1.1.36.2.2.2"> <csymbol cd="ambiguous" id="p1.1.m1.1.36.2.2.2.1.cmml" xref="p1.1.m1.1.36.2.2.2">subscript</csymbol> <ci id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4">𝑔</ci> <ci id="p1.1.m1.1.5.1.cmml" xref="p1.1.m1.1.5.1">𝑛</ci> </apply> </apply> <apply id="p1.1.m1.1.36.2.3.cmml" xref="p1.1.m1.1.36.2.3"> <times id="p1.1.m1.1.36.2.3.1.cmml" xref="p1.1.m1.1.36.2.3.1"/> <apply id="p1.1.m1.1.7.cmml" xref="p1.1.m1.1.7"> <divide id="p1.1.m1.1.7.1.cmml" xref="p1.1.m1.1.7"/> <cn type="integer" id="p1.1.m1.1.7.2.cmml" xref="p1.1.m1.1.7.2">1</cn> <apply id="p1.1.m1.1.7.3.cmml" xref="p1.1.m1.1.7.3"> <times id="p1.1.m1.1.7.3.4.cmml" xref="p1.1.m1.1.7.3.4"/> <cn type="integer" id="p1.1.m1.1.7.3.1.cmml" xref="p1.1.m1.1.7.3.1">2</cn> <ci id="p1.1.m1.1.7.3.2.cmml" xref="p1.1.m1.1.7.3.2">𝜋</ci> <ci id="p1.1.m1.1.7.3.3.cmml" xref="p1.1.m1.1.7.3.3">𝑖</ci> </apply> </apply> <apply id="p1.1.m1.1.36.2.3.2.cmml" xref="p1.1.m1.1.36.2.3.2"> <apply id="p1.1.m1.1.36.2.3.2.1.cmml" xref="p1.1.m1.1.36.2.3.2.1"> <csymbol cd="ambiguous" id="p1.1.m1.1.36.2.3.2.1.1.cmml" xref="p1.1.m1.1.36.2.3.2.1">subscript</csymbol> <int id="p1.1.m1.1.8.cmml" …
Symbols used: the ratio of the circumference of a circle to its diameter
Symbols used: differential of x
Symbols used: base of natural logarithm
Symbols used: imaginary unit
Symbols used: integral
Symbols used: analytic function
Symbols used: coefficients
Symbols used: radious of annulus
Symbols used: comparison function
instance of: Digital Library of Mathematical Functions Formula
MaRDI profile type: MaRDI formula profile