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Digital Library of Mathematical Functions ID
2.5.E4
ℳ
I
(
z
)
=
ℳ
f
(
1
-
z
)
ℳ
h
(
z
)
.
Mellin-transform
𝐼
𝑧
Mellin-transform
𝑓
1
𝑧
Mellin-transform
ℎ
𝑧
{\displaystyle{\displaystyle\mathscr{M}\mskip-3.0mu I\mskip 3.0mu \left(z% \right)=\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z\right)\mathscr{M}% \mskip-3.0mu h\mskip 3.0mu \left(z\right).}}
Constraint(s)
Symbols List
ℳ
(
f
)
(
s
)
Mellin-transform
𝑓
𝑠
{\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
: Mellin transform
f
(
x
)
𝑓
𝑥
{\displaystyle{\displaystyle f(x)}}
: locally integrable function
I
(
x
)
𝐼
𝑥
{\displaystyle{\displaystyle I(x)}}
: convolution integral
h
(
x
)
ℎ
𝑥
{\displaystyle{\displaystyle h(x)}}
: function
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