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shichi
Hyperbolic sine and cosine integrals.SYNOPSIS:
double x, Chi, Shi, shichi();
shichi(x, &Chi, &Shi);
DESCRIPTION:
Approximates the integrals
x
-
| | cosh t - 1
Chi(x) = eul + ln x + | ----------- dt,
| | t
-
0
x
-
| | sinh t
Shi(x) = | ------ dt
| | t
-
0
where eul = 0.57721566490153286061 is Euler's constant. The integrals are evaluated by power series for x < 8 and by Chebyshev expansions for x between 8 and 88. For large x, both functions approach exp(x)/2x. Arguments greater than 88 in magnitude return MAXNUM.
ACCURACY:
Test interval 0 to 88.
Relative error:
arithmetic function # trials peak rms
DEC Shi 3000 9.1e-17
IEEE Shi 30000 6.9e-16 1.6e-16
Absolute error, except relative when |Chi| > 1:
DEC Chi 2500 9.3e-17
IEEE Chi 30000 8.4e-16 1.4e-16