Incomplete Gamma Function of the Second Kind

05262021, 12:32 AM
Post: #2




RE: Incomplete Gamma Function of the Second Kind
(05252021 10:26 PM)toml_12953 Wrote: "This function works only in radian mode Error: Bad Argument Value" 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^(a1)*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 

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Incomplete Gamma Function of the Second Kind  toml_12953  05252021, 10:26 PM
RE: Incomplete Gamma Function of the Second Kind  Albert Chan  05262021 12:32 AM

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