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The formulas j_n(z) = z^n(-1/zd/(dz))^n(sinz)/z (1) y_n(z) = -z^n(-1/zd/(dz))^n(cosz)/z (2) for n=0, 1, 2, ..., where j_n(z) is a spherical Bessel function of the first kind ...

A real function is said to be analytic if it possesses derivatives of all orders and agrees with its Taylor series in a neighborhood of every point.

The real axis is the line in the complex plane corresponding to zero imaginary part, I[z]=0. Every real number corresponds to a unique point on the real axis.

A function whose range is in the real numbers is said to be a real function, also called a real-valued function.

A real matrix is a matrix whose elements consist entirely of real numbers. The set of m×n real matrices is sometimes denoted R^(m×n) (Zwillinger 1995, p. 116).

A polynomial having only real numbers as coefficients. A polynomial with real coefficients is a product of irreducible polynomials of first and second degrees.

A variable that may assume only real values.

A vector whose elements are real numbers.

A real vector space is a vector space whose field of scalars is the field of reals. A linear transformation between real vector spaces is given by a matrix with real entries ...

"The reals" is a common way of referring to the set of real numbers and is commonly denoted R.