hp40g+.book Page 67 Friday, December 9, 2005 1:03 AM

Typing:

 

 

 

⎛ ---------------------------

1

+ (X–6) ⋅ a + b⎞

 

⎜ X2

– 6X + 9

⎟

LAP⎜------------------------------------------------------------------

X2–6X+ 9

⎟

⎜

 

⎟

⎝

 

 

⎠

 

gives:

 

 

 

 

⎛x3

⎞

⋅ e

3x

 

----

– (3a – b) ⋅ x + a

 

 

⎝ 6

⎠

 

 

LAP

See ILAP above.

 

 

PA2B2

Decomposes a prime integer p congruent to 1 modulo 4,

 

as follows:

 

 

 

p = a2 + b2.

 

 

 

The calculator gives the result as a + b · i.

 

Example 1

 

 

 

Typing:

 

 

 

 

PA2B2(17)

 

 

 

gives:

 

 

 

 

4 + i

 

 

 

that is, 17 = 42 + 12

 

 

 

Example 2

 

 

 

Typing:

 

 

 

 

PA2B2(29)

 

 

 

gives:

 

 

 

 

5 + 2 · i

 

 

 

that is, 29 = 52 + 22

 

 

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)

Computer Algebra System (CAS)

14-67