Quantum Gravity 284.99: Notice that 298.98 has terms in 1/t, B - 1/t = (Bt - 1)/t, and t
OsherD
Notice that 284.99 is:
1) dy/dt = A/(tyo) + (Bt - 1)y/t + Cy(0)ty^2
which has terms on the right hand side in 1/t, (Bt - 1)/t, and t
respectively, which are the "central" terms of a real Laurent Series
truncated at terms with powers higher than 1 or lower than -1, the
middle term (Bt - 1)/t being B - 1/t so the order is 1/t, B (say,
constant for simplicity), t for the respective powers of t from -1 to
0 to +1.
We could of course have simply proposed a truncated model of the
Riccati Differential Equation consisting of coefficients in "central 3
powers of t from -1 through +1 of the Laurent Series", but the
derivation as well is rather surprising in revealing its connection
with the Volterra-like convolution. Again, A, B, C most simply relate
to this by being chosen as some simple constants like 1, 1, -1
respectively, unless there is some particular reason for choosing them
as more complicated functions of t.
Osher Doctorow
OsherD
I meant to refer to 284.98, not 294.98 in the previous post.
Osher Doctorow