HP Prime Collection of Functions

[Eddie W. Shore]

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

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

Code:


// 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