HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 239
Legendre, Partfrac
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hp40g+.book Page 57 Friday, December 9, 2005 1:03 AM LCM LEGENDRE PARTFRAC Returns the LCM (Least Common Multiple) of two polynomials. Example Typing: LCM(X2 + 2·X + 1, X2 - 1) gives: (x2 + 2x + 1) ⋅ (x - 1) Returns the polynomial Ln, a non-null solution of the differential equation: (x2 - 1) ⋅ y″ - 2 ⋅ x ⋅ y′ - n(n + 1) ⋅ y = 0 where n is a whole number. Example Typing: LEGENDRE(4) gives: -3--5-----⋅---x---4---------3---0-----⋅---x---2---+-----3-8 Returns the partial fraction decomposition of a rational fraction. Example Typing: ARTFRAC ⎛ ⎜ ⎝ X----5---------2----X---3----+-----1 X4 - 2X3 + 2X2 - 2X + 1 gives, in real and direct mode: x + 2 + ----x---------3----2x2 + 2 + ---------1-----2x - 2 and gives, in complex mode: 1----------3-----⋅---i -----1- 1-----+-----3----⋅---i x + 2 + --------4 2 4---------- x+i x-1 x-i Computer Algebra System (CAS) 14-57