Bernoulli(n, [z])
n
Positive integer.

[z]
Real or complex number.

Description
Returns the nth Bernoulli number n.

If z is given, returns the nth Bernoulli polynomial of z.

Examples
Bernoulli(3, a)
a
3
-
3
a
2
2
+
a
2
Bernoulli(n, 1/2)
-
Bernoulli
(
n
)
+
2
(
-
n
+
1
)
Bernoulli
(
n
)
Bernoulli(n, 3)
n
+
n
2
(
n
-
1
)
+
Bernoulli
(
n
)
Bernoulli(n, -z)
(
-1
)
n
Bernoulli
(
n
,
z
)
+
n
z
(
n
-
1
)
(
-1
)
n
Bernoulli(n, 5)
n
+
n
4
(
n
-
1
)
+
n
3
(
n
-
1
)
+
n
2
(
n
-
1
)
+
Bernoulli
(
n
)
Bernoulli(n, -5)
n
5
n
(
-1
)
n
5
+
(
-1
)
n
Bernoulli
(
n
)
+
n
(
-1
)
n
+
n
4
(
n
-
1
)
(
-1
)
n
+
n
3
(
n
-
1
)
(
-1
)
n
+
n
2
(
n
-
1
)
(
-1
)
n
Bernoulli(3, 5)
90
Bernoulli(4, 5)
11999
30

References

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