D

#### Don Lancaster

- Jan 1, 1970

- 0

function of one sort or another to its underlying series form.

But how can you get from a known accurate series expression to a

nonobvious and crucially esoteric equivalent function?

Specifically, the "raw" power series

[-1517.83 5094.6 821.18 -29457.7 61718.9 -61268.8 30448.6 -4770.84

-269.684 -2892.14 3300.63 -1460.88 213.578 78.8959 -49.2164 12.3083

-1.74731 0.149743 -0.00245142 0.103691]

where 0.103691 is the x^0 term, -0.00245142 is x^1 etc...

The equivalent McLauran Series (or Taylor about zero) is found by

dividing each term by its factorial. 0.103691/1! , -0.00245142/2!...

... may be of extreme interest in finding a closed form expression

that involves trig products and possibly exponantials. The range of

interest is from 0 to 1.

The function appears continuous and monotonic with well behaved derivatives.

The trig angle of 84.0000 degrees is also expected to play a major role

in the solution. As is the trig identity of cos(a+b) = cos(a)cos(b) -

sin(a)sin(b). As is a magic constant of 0.104528. Everything happens in

the first quadrant.

Sought after is a closed form determnistic solution that accepts the 0-1

value, the 84 degree angle, and the magic constant that evaluates to the

above series.

--

Many thanks,

Don Lancaster voice phone: (928)428-4073

Synergetics 3860 West First Street Box 809 Thatcher, AZ 85552

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