## Wednesday, January 31, 2018

### HP Prime Collection of Functions

HP Prime Collection of Functions

Introduction

The program COLLECTION has 13 historical, archaic, and unusual functions.  They are:

 Name Function and Syntax Formula Used Versine VERS(X) 1 – cos x Coversine COVERS(X) 1 – sin x Haversine HAV(X) sin(x/2)^2 Normalized Sampling NSINC(X) sin(π * x)/(π * x) Exsecant EXSEC(X) sec x - 1 Gundermannian GD(X) atan(sinh x) Inverse Gundermannian INVGD(X) asinh(tan x) Dilogarithm DILN(X) ∫ (ln t / (t – 1) dt, 1, x) Exponential Polynomial EPOLY(N, X) Σ(x^j / j!, j, 0, n) Hypotenuse of a Right Triangle HYPER(A,B) √(a^2 + b^2) Langevin Function LANGEVIN(X) 1/tanh x – 1/x General Mean Function GENMEAN(N,A,B) N = 1, arithmetic mean N = 2, root mean square N = -1, harmonic mean ((a^n + b^n) / 2)^(1/n) Logarithmic Integral Li(X) Ei(LN(x))

Note:  All the functions listed above can be called separately.  Note that there is no COLLECTION program per se, it is file that contains all the functions.

HP Prime Program: COLLECTION

// 2018-01-28 EWS
// A collection of functions
// An Atlas of Functions-2nd Ed-2009

// Note the COLLECTION is a file
// EXPORT can't have a ; attached in this case

EXPORT VERS(X)
BEGIN
// versine
RETURN 1-COS(X);
END;

EXPORT COVERS(X)
BEGIN
// coversine
RETURN 1-SIN(X);
END;

EXPORT HAV(X)
BEGIN
// haversine
RETURN SIN(X/2)^2;
END;

EXPORT NSINC(X)
BEGIN
// normalized sampling
RETURN SIN(π*X)/(π*X);
END;

EXPORT EXSEC(X)
BEGIN
// exsecant
RETURN SEC(X)-1;
END;

EXPORT GD(X)
BEGIN
// Gundermannian
RETURN ATAN(SINH(X));
END;

EXPORT INVGD(X)
BEGIN
// Inverse Gundermannian
RETURN ASINH(TAN(X));
END;

EXPORT DILN(X)
BEGIN
// dilogarithm
RETURN ∫(LN(T)/(T-1),T,1,X);
END;

EXPORT EPOLY(N,X)
BEGIN
// exponential polynomial
// order, value
RETURN Σ(X^J/J!,J,0,N);
END;

EXPORT HYPER(A,B)
BEGIN
// hypotonuse of a right
// triangle
RETURN √(A^2+B^2);
END;

EXPORT LANGEVIN(X)
BEGIN
// Langevin function
RETURN 1/TANH(X)-1/X;
END;

EXPORT GENMEAN(N,A,B)
BEGIN
// General mean
// N = 1, arithmetic mean
// N = 2, root mean square
// N = −1, harmonic mean
RETURN ((A^N+B^N)/2)^(1/N);
END;

EXPORT Li(X)
BEGIN
// Logathmic Integral
RETURN CAS.Ei(LN(X));
END;

Source:

Keith Oldham, Jan Myland, and Jerome Spainer.  An Atlas of Functions  2nd Edition.  Springer:  New York.  2009  e-ISBN 978-0-387-48807-3

Eddie

This blog is property of Edward Shore, 2018.