# Revision history [back]

Probably there is more to it than this, but why not just do

from sage.symbolic.integration.integral import indefinite_integral
h(x,t) = sqrt(t)*exp((1+t)*x)*bessel_I(1,2*sqrt(t)*x)
egf = 1 + indefinite_integral(h,x)
taylor(egf, x, 0, 6)


This may not do it for you, but hopefully removes the error in question. Lambdas may not play well with integration.

Probably there is more to it than this, but why not just do

from sage.symbolic.integration.integral import indefinite_integral
h(x,t) = sqrt(t)*exp((1+t)*x)*bessel_I(1,2*sqrt(t)*x)
egf = 1 + indefinite_integral(h,x)
taylor(egf, x, 0, 6)


This may not do it for you, but hopefully removes the error in question. Lambdas may not play well with integration.

Edit: probably the error was caused by using the indefinite integral directly.

sage: h(x,t) = sqrt(t)*exp((1+t)*x)*bessel_I(1,2*sqrt(t)*x)
sage: egf = integrate(h,x) + 1


works fine. However,

sage: egf
(x, t) |--> sqrt(t)*integrate(bessel_I(1, 2*sqrt(t)*x)*e^((t + 1)*x), x) + 1


so Sage doesn't know how to do much with that, as the error message

sage: taylor(egf, x, 0, 6)
TypeError: ECL says: Error executing code in Maxima: taylor: unable to expand at a point specified in:
'integrate(bessel_i(1,2*sqrt(t)*x)*%e^((t+1)*x),x)


indicates. And the other way to get series (there is another, from Ginac) yields not much better:

sage: egf.series(x==0, 6)
AttributeError: 'MaximaLibElement' object has no attribute '_name'


since it doesn't know what to do with an unevaluated integral.

There may yet be a workaround, but I'm not conversant enough with this to say what it would be.