Incomplete Gamma Function of the Second Kind

[Albert Chan]

(05-25-2021 10:26 PM)toml_12953 Wrote:  "This function works only in radian mode Error: Bad Argument Value"

It doesn't use any trig functions that I can see so why the error?

Depending on user input, CAS might not recognize it related to gamma function.
It may tried to remove infinity by substitution, x = tan(t), so that x→∞ map to t→pi/2

CAS> gamma1(a,x) := int(t^(a-1)*e^-t, t=x .. inf)

CAS> gamma1(1, i)       → e^-i
CAS> gamma1(1.0, i)    → integrate(tan(t)^0.*e^(-tan(t))*(1+tan(t)^2), t, atan(i), π/2)

Actually, x=tan(t) here just shift the infinity ... atan(i)

Does atan(i) even have a limit ? CAS seems to think it is just a value.

CAS> limit(atan(x),x=i)    → ATAN(i)

Ref: DLMF: Chapter 8 Incomplete Gamma and Related Functions