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Positive zero of the digamma function
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Mathematics
Area of mathematics
Analysis
Complex analysis
Gamma function
Digamma function
Created
2026-09-24
Updated
2026-09-24
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The
digamma function
is strictly increasing on the positive real axis, while
ψ
(
1
)
=
−
γ
<
0
,
ψ
(
2
)
=
1
−
γ
>
0.
(1)
It therefore has exactly one positive zero, and that zero lies in
(
1
,
2
)
.
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(7)
Digamma function
Gamma function
Complex analysis
Analysis
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2023
/
ii
/
Paper 1
/
7E
/
Solution
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