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Gamma function evaluation with arbitrary precision

Nicolas Legnazzi
Posted 4 years ago

Hello, I am a Physics student and I am trying to get values of incomplete Gamma function with arbitrary precision. On the Mathematica page they clarify that the Gamma function can be evaluated with arbitrary precision. I have the 11.1.1 version of Mathematica and I am entering the following code to evaluate with 64 digits:

N[Gamma[3.33, 10.14], 64]

However the result appears with 18 digits:

0.010989671959126465

Is there a way to get it with at least 32 digits? Thank you.
POSTED BY: Nicolas Legnazzi
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POSTED BY: Nicolas Legnazzi

Maybe:

  f[k_, r_] := LaguerreL[SetPrecision[k, 100], 2, SetPrecision[r, 100]]
  f[3.33, 10.14]

  (*-16.253378012832750669487606211204418150244508376350192594107493361445\
  8686734122774716077406778543804*)
POSTED BY: Mariusz Iwaniuk

Thanks! You solved my problem!
POSTED BY: Nicolas Legnazzi

Since your arguments only have machine precision the output will be limited to machine precision. If you input the arguments with more precision this will then be automatically be used throughout the calculation:

Gamma[3.33`100, 10.14`100]
POSTED BY: Sander Huisman

Brilliant! Many thanks. You have solved my problem, now I will be able to continue investigating. Thank you again.
POSTED BY: Nicolas Legnazzi
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