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Past exam of the algebra and analysis I for mathematics and philosophy course of the University of Oxford
/
2013
/
Analysis
/
6
/
a
/
iv
/
Solution
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Past exam of the algebra and analysis I for mathematics and philosophy course of the University of Oxford
2013
Analysis
6
a
iv
2026-10-31
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A
zero
of order
n
≥
1
at
a
means
that
f
is holomorphic near
a
and
f
(
a
)
=
f
′
(
a
)
=
⋯
=
f
(
n
−
1
)
(
a
)
=
0
,
f
(
n
)
(
a
)
=
0.
(1)
Equivalently its
Taylor series
starts with the nonzero
coefficient
of
(
z
−
a
)
n
, so
f
(
z
)
=
(
z
−
a
)
n
h
(
z
)
,
h
holomorphic near
a
,
h
(
a
)
=
0.
(2)
Unlike
a
pole
,
a
zero is
a
regular point of the
function
itself; its reciprocal
has a
pole
of the corresponding order.
Ancestors
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iv
a
6
Analysis
2013
Past exam of the algebra and analysis I for mathematics and philosophy course of the University of Oxford
Algebra and analysis I for mathematics and philosophy course of the University of Oxford
Year 2 of the mathematics and philosophy course of the University of Oxford
Mathematics and philosophy course of the University of Oxford
Undergraduate course of the University of Oxford
Course of the University of Oxford
University of Oxford
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