## Wednesday, November 29, 2017

### Casio fx-5800p Special Functions

Casio fx-5800p Special Functions

Programs

An Alternate Way of Extracting the Fraction and Integer Parts of a Number

The fraction part is stored in F, and the integer part is stored in I.  This algorithm can be used when a calculator or programming language does not have a fractional part or integer part function.

This program assumes the program is in Radians mode.

Casio fx-5800P Program FPIP

0.5    → F
? → X
cos(πX) = 0 Goto 1
Abs(X) → F
tan^-1 (tan (πF)) ÷ π → F
X < 0 -F → F
Lbl 1
F /right-triangle ([Shift] [x^2])
X – F → I

Bernoulli Numbers

The program BERNOULLI approximates the Bernoulli number of nth order.

Casio fx-5800P Program BERNOULLI

? → N
If N = 0
Then
1 → B
Goto 1
IfEnd
If Frac(N ÷ 2) ≠ 0
Then
Int( Abs(N – 2) ÷ (N – 2) – 1) ÷ 4 → B
Goto 1
IfEnd
Σ ( (2*J*π)^(-N), J, 1, 250) * (-1)^(N ÷ 2 + 1) * 2 * N! → B
Lbl 1
B

Euler Numbers

The program EULERNUM calculates the Euler number of order n.

Casio fx-5800P Program EULERNUM

? → N
0 → E
Frac(N ÷ 2) ≠ 0 Goto 1
(2 ÷ π)^(N + 1) * N! ÷ 5 → E
-1 – 10 * Int(E) → E
Frac(N ÷ 4) ≠ 0 Goto 1
4 – E → E
N ≠ 0 Goto 1
1   → E
Lbl 1
E

Custom Formulas

How to create custom formulas:  [MODE], 5.  PROG, 1.  NEW, give the name, 3. Formula

To calculate the custom formula, press [CALC], enter the value for T (ignore X because X is a dummy variable).

Sine Integral:   SI:  ∫( sin(X)/X dX,0,T)

Dawson Integral:  DAWSON:  ∫(e^(T^2-X^2) dX,0,T)

Bessel Function, with order N:  BESSEL:  1/π * ∫(cos(T * sin(X)-N*X) dX,0,T)

Error Function:  ERF:  2/√π * ∫(e^(-X^2) dX,0,T)

Fresnel Sine:  FRESSIN:  ∫( sin(π*X^2/2) dX,0,T)

Fresnel Cosine: FRESCOS: ∫( cos(π*X^2/2) dX,0,T)

Source:

Jerome Spainer and Keith B. Oldham  An Atlas of Functions Hemisphere Publication Corporation: Washington  1987  ISBN 0-89116-5738-8

Eddie

This blog is property of Edward Shore, 2017