E407: Summation of Chebyshev Series

Author(s): K.S. Kölbig	Library: MATHLIB
Submitter:	Submitted: 24.01.1986
Language: Fortran	Revised: 15.11.1995

Function subprograms RCHSUM and DCHSUM compute, for real arguments x in the specified intervals, one of the following four sums:

where is the Chebyshev polynomial of degree n and .

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

Structure:

FUNCTION subprograms
User Entry Names: RCHSUM, DCHSUM
Obsolete User Entry Names: CHSUM RCHSUM

Usage:

In any arithmetic expression,

RCHSUM(MODE,C,N,X) or DCHSUM(MODE,C,N,X)

has the value of the sum selected by MODE. RCHSUM is of type REAL, and DCHSUM is of type DOUBLE PRECISION. C and X have the same type as the function name. MODE and N are of type INTEGER.

MODE

Type of sum to be evaluated .

C

One-dimensional array with dimension (0:d), , containing the coefficients
.

N

Limit N of summation.

X

Argument x.

Notes:

Note that some authors use a different definition for the constant term in (1), (2) and (4), i.e. instead of . Here, the definition of Ref. 1 is used.

References:

1. Y.L. Luke, Mathematical functions and their approximations, (Academic Press, New York 1975)
2. C.W. Clenshaw, Chebyshev series for mathematical functions, Mathematical Tables, Vol.5 (National Physical Laboratory, London, 1962).