HP 40gs - Manual (Page 249)

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 nth 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
6X – 9 +
---------------------------- X 6 – ( ) a b + ⋅ +
X
2
6X – 9 +
-------------------------------------------------------------------
⎝ ⎠
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎛ ⎞
x
3
6
----- 3a b – ( ) – x a + ⋅
⎝ ⎠
⎛ ⎞ e 3x ⋅
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