HP Prime Collection of Functions - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Software Libraries (/forum-10.html) +--- Forum: HP Prime Software Library (/forum-15.html) +--- Thread: HP Prime Collection of Functions (/thread-10066.html) HP Prime Collection of Functions - Eddie W. Shore - 02-01-2018 04:48 AM 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