On 2017-03-21 15:58, Henry Baker wrote:
Maxima works:
a=-1/2,b=-3/8,c=-3/16,d=-45/128,e=-63/256,f=-375/1024, ...
At 03:01 PM 3/21/2017, David Wilson wrote:
Let
f(x)^2 = f(x^2) - 1
and assume f is of the form
f(x) = x + a x^-1 + b x^-3 + c x^-5 + ...
What are the first few coefficients (say 20) as rational numbers?
With the tools I have, it would take me a while to power through this. I assume it would be easier with a symbolic math program.
OEIS A088674 Out[8]= 1 - 1/2 x (1 + (3 x)/4 + (3 x^2)/8 + (45 x^3)/64 + (63 x^4)/128 + ( 375 x^5)/512 + (699 x^6)/1024 + (19389 x^7)/16384 + (37947 x^8)/ 32768 + (224781 x^9)/131072 + (506949 x^10)/262144 + ( 6105897 x^11)/2097152 + (14473899 x^12)/4194304) In[9]:= %^2 - (% /. x -> x^2) // Expand Out[9]= -x + (83196831 x^14)/16777216 + (31624083 x^15)/8388608 + . . . --rwg