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8 Incomplete Gamma and Related FunctionsComputation

§8.26 Tables

  1. §8.26(i) Introduction
  2. §8.26(ii) Incomplete Gamma Functions
  3. §8.26(iii) Incomplete Beta Functions
  4. §8.26(iv) Generalized Exponential Integral

§8.26(i) Introduction

For tables published before 1961 see Fletcher et al. (1962) and Lebedev and Fedorova (1960).

§8.26(ii) Incomplete Gamma Functions

  • Khamis (1965) tabulates P(a,x) for a=0.05(.05)10(.1)20(.25)70, 0.0001x250 to 10D.

  • Pagurova (1963) tabulates P(a,x) and Q(a,x) (with different notation) for a=0(.05)3, x=0(.05)1 to 7D.

  • Pearson (1965) tabulates the function I(u,p) (=P(p+1,u)) for p=1(.05)0(.1)5(.2)50, u=0(.1)up to 7D, where I(u,up) rounds off to 1 to 7D; also I(u,p) for p=0.75(.01)1, u=0(.1)6 to 5D.

  • Zhang and Jin (1996, Table 3.8) tabulates γ(a,x) for a=0.5,1,3,5,10,25,50,100, x=0(.1)1(1)3,5(5)30,50,100 to 8D or 8S.

§8.26(iii) Incomplete Beta Functions

  • Pearson (1968) tabulates Ix(a,b) for x=0.01(.01)1, a,b=0.5(.5)11(1)50, with ba, to 7D.

  • Zhang and Jin (1996, Table 3.9) tabulates Ix(a,b) for x=0(.05)1, a=0.5,1,3,5,10, b=1,10 to 8D.

§8.26(iv) Generalized Exponential Integral

  • Abramowitz and Stegun (1964, pp. 245–248) tabulates En(x) for n=2,3,4,10,20, x=0(.01)2 to 7D; also (x+n)exEn(x) for n=2,3,4,10,20, x1=0(.01)0.1(.05)0.5 to 6S.

  • Chiccoli et al. (1988) presents a short table of Ep(x) for p=92(1)12, 0x200 to 14S.

  • Pagurova (1961) tabulates En(x) for n=0(1)20, x=0(.01)2(.1)10 to 4-9S; exEn(x) for n=2(1)10, x=10(.1)20 to 7D; exEp(x) for p=0(.1)1, x=0.01(.01)7(.05)12(.1)20 to 7S or 7D.

  • Stankiewicz (1968) tabulates En(x) for n=1(1)10, x=0.01(.01)5 to 7D.

  • Zhang and Jin (1996, Table 19.1) tabulates En(x) for n=1,2,3,5,10,15,20, x=0(.1)1,1.5,2,3,5,10,20,30,50,100 to 7D or 8S.