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Chebyshev Polynomial for the HP-65

This program is Copyright © 1974 by Hewlett-Packard and is used here by permission. This program was originally published in the HP-65 Math Pac 2.

This program is supplied without representation or warranty of any kind. Hewlett-Packard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

Card Labels
Chebyshev Polynomial
Label Tn(x)                
Key A B C D E

Overview

This program computes the value of the Chebyshev polynomial Tn(x) by using the recurrence equation

          Tn+1(x) = 2xTn(x) - Tn-1(x)

where starting values are T0(x) = 1,  T1(x) = x and n is a nonnegative integer.

Instructions

Step Instructions Input Data/Units Keys Output Data/Units
1 Enter Program      
2    n ENTER↑  
3   x A Tn(x)

Example

T3 (0.4) = -0.94

The Program

 CODE  KEYS
   23  LBL
   11  A
33 01  STO 1
   02  2
33 02  STO 2
   71  ×
33 03  STO 3
   44  CLX
35 07  g x⇔y
35 22  g x≤y
   01  1
   24  RTN
   01  1
33 04  STO 4
35 23  g x=y
34 01  RCL 1
   24  RTN

   23  LBL
   01  1
   44  CLX
34 03  RCL 3
34 01  RCL 1
   71  ×
34 04  RCL 4
35 00  g LST X
33 04  STO 4
35 08  g R↓
   51  -
33 01  STO 1
   44  CLX
34 02  RCL 2
   01  1
   61  +
33 02  STO 2
35 22  g x≤y
   22  GTO
   01  1
34 01  RCL 1
   24  RTN
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP
35 01  g NOP

Register Use

R1  used
R2  used
R3  2x
R4  used
R5  
R6  
R7  
R8  
R9  used

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