Asymptotic and exact series representations for the incomplete Gamma function

@article{Amore2005AsymptoticAE,
  title={Asymptotic and exact series representations for the incomplete Gamma function},
  author={P. Amore},
  journal={EPL},
  year={2005},
  volume={71},
  pages={1-7}
}
  • P. Amore
  • Published 2005
  • Mathematics, Physics
  • EPL
Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly convergent series, completely analytical, which can be used to obtain arbitrarily accurate estimates of Γ(a,x) for any value of a or x. Applications of these formulas are discussed. 

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References

SHOWING 1-10 OF 16 REFERENCES
A method for classical and quantum mechanics
CALCULATING NORMAL PROBABILITIES
Large Order Perturbation Theory and Summation Methods in Quantum Mechanics
Path Integrals in Quantum Mechanics Statistics and Polymer Physics
Phys
  • Rev. D 23, 2916
  • 1981
Phys
  • Rev. D 63, 125013
  • 2001
Phys. Rev. D
  • Phys. Rev. D
  • 2001
The incomplete gamma functions since Tricomi
  • “Tricomi’s Ideas and Contemporary Applied Mathematics”, Atti Convegni Lincei, Vol. 147, Accad. Naz. Lincei, Rome
  • 1998
Tricomi's ideas and contemporary applied mathematics
Calculating normal probabilities, The American Mathematical Montly
  • Calculating normal probabilities, The American Mathematical Montly
  • 1995
...
1
2
...