HP 40gs, User Manual

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Computer Algebra System (CAS) 14-67
Typing:
gives:
LAP
See ILAP above.
PA2B2
Decomposes a prime integer p congruent to 1 modulo 4,
as follows:
p = a
2
+ b
2
.
The calculator gives the result as a + b · i.
Example 1
Typing:
PA2B2(17)
gives:
4 + i
that is, 17 = 4
2
+ 1
2
Example 2
Typing:
PA2B2(29)
gives:
5 + 2 · i
that is, 29 = 5
2
+ 2
2
PSI
Returns the value of the n th derivative of the Digamma
function at a .
The Digamma function is the derivative of ln(
Γ
(x)).
Example
Typing:
PSI(3, 1)
ILAP
1
X
2
6 X – 9 +
----------------------------
X 6 –
( )
a b +
⋅
+
X
2
6 X – 9 +
-------------------------------------------------------------------
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎛ ⎞
x
3
6
-----
3 a b –
( )
– x a +
⋅
⎝ ⎠
⎛ ⎞
e
3 x
⋅
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