E409: Summation of Trigonometric Series

Author(s): T. Håvie, K.S. Kölbig	Library: MATHLIB
Submitter:	Submitted: 01.12.1994
Language: Fortran	Revised:

Function subprograms RTRGSM and DTRGSM compute the sum of the trigonometric series

for a given argument x in the range and given coefficients .

On CDC and Cray computers, the double-precision version DTRGSM is not available.

Structure:

FUNCTION subprogram
User Entry Names: RTRGSM, DTRGSM

Usage:

In any arithmetic expression, for (type REAL), (type DOUBLE PRECISION),

    tTRGSM(X,A,N,B,M,IOP)

has the value f(x).

X

(Type according to t) Argument x.

A

(Type according to t) One-dimensional array of dimension (0:d) where , containing the constant coefficient in A(0) and the cosine coefficients in A(k).

N

(INTEGER) The number n of cosine coefficients.

B

(Type according to t) One-dimensional array of length , containing the sine coefficients in B(k).

M

(INTEGER) The number m of sine coefficients.

IOP

(INTEGER) An option number:
the general case,
all are zero, i.e. f(x)=f(-x),
all are zero, i.e. f(x)=-f(-x).

Method:

Standard recurrence relations are used for calculating the sum (see Ref. 1).

Notes:

For a function f(z) given in the range , use the transformation

References:

1. W. Clenshaw, A note on the summation of Chebyshev series, MTAC (later renamed Math. Comp.) 9 (1955) 118-120.