xlifepp – Functions – J

j_s

inline complex_t xlifepp::j_s(const complex_t &z, real_t x, const complex_t &q)

Parameters:

q – exp(-ixz) /(w2’(z)-qw2(z))

jacobiPolynomials

void xlifepp::jacobiPolynomials(real_t a, real_t b, real_t, std::vector<real_t>&)

Jacobi polynomials on [-1, 1] up to order n P_0 = 1, P_1 = (2*(a+1)+(a+b+2)*(x-1)) / 2 P_{n+1}*{ 2*(n+1)(n+a+b+1)(2*n+a+b) } = { (2*n+1+a+b)(a^2-b^2) + (2*n+a+b)(2*n+1+a+b)(2*n+2+a+b)*x } * P_{n} -{ 2*(n+a)*(n+b)(2*n+2+a+b) } * P_{n-1} , n > 0.

jacobiPolynomials01

void xlifepp::jacobiPolynomials01(real_t a, real_t b, real_t, std::vector<real_t>&)

Jacobi polynomials on [0, 1] up to order n.

jacobiPolynomialValue

static real_t xlifepp::jacobiPolynomialValue(number_t n, real_t a, real_t b, real_t x)

Jacobi polynomial P_n^(a,b)(x) by the three term recurrence (Abramowitz & Stegun 22.7.1)

join

inline string_t xlifepp::join(const Strings &ss, const string_t &delim)

join utility

jump

OperatorOnUnknown &xlifepp::jump(const Unknown &un)

OperatorOnUnknown &xlifepp::jump(OperatorOnUnknown &opu)