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))

Radians mode is assumed. 

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  2^nd Edition.  Springer:  New York.  2009  e-ISBN 978-0-387-48807-3

Eddie

This blog is property of Edward Shore, 2018.