Digital Library of Mathematical Functions
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8 Incomplete Gamma and Related FunctionsComputation

§8.26 Tables

Contents

§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 \mathop{P\/}\nolimits\!\left(a,x\right) for a=0.05(.05)10(.1)20(.25)70, 0.0001\leq x\leq 250 to 10D.

  • Pagurova (1963) tabulates \mathop{P\/}\nolimits\!\left(a,x\right) and \mathop{Q\/}\nolimits\!\left(a,x\right) (with different notation) for a=0(.05)3, x=0(.05)1 to 7D.

  • Pearson (1965) tabulates the function I(u,p) (=\mathop{P\/}\nolimits\!\left(p+1,u\right)) for p=-1(.05)0(.1)5(.2)50, u=0(.1)u_{p} to 7D, where I(u,u_{p}) 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 \mathop{\gamma\/}\nolimits\!\left(a,x\right) 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 \mathop{I_{{x}}\/}\nolimits\!\left(a,b\right) for x=0.01(.01)1, a,b=0.5(.5)11(1)50, with b\leq a, to 7D.

  • Zhang and Jin (1996, Table 3.9) tabulates \mathop{I_{{x}}\/}\nolimits\!\left(a,b\right) 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 \mathop{E_{{n}}\/}\nolimits\!\left(x\right) for n=2,3,4,10,20, x=0(.01)2 to 7D; also (x+n)e^{x}\mathop{E_{{n}}\/}\nolimits\!\left(x\right) for n=2,3,4,10,20, x^{{-1}}=0(.01)0.1(.05)0.5 to 6S.

  • Chiccoli et al. (1988) presents a short table of \mathop{E_{{p}}\/}\nolimits\!\left(x\right) for p=-\tfrac{9}{2}(1)-\tfrac{1}{2}, 0\leq x\leq 200 to 14S.

  • Pagurova (1961) tabulates \mathop{E_{{n}}\/}\nolimits\!\left(x\right) for n=0(1)20, x=0(.01)2(.1)10 to 4-9S; e^{x}\mathop{E_{{n}}\/}\nolimits\!\left(x\right) for n=2(1)10, x=10(.1)20 to 7D; e^{x}\mathop{E_{{p}}\/}\nolimits\!\left(x\right) for p=0(.1)1, x=0.01(.01)7(.05)12(.1)20 to 7S or 7D.

  • Stankiewicz (1968) tabulates \mathop{E_{{n}}\/}\nolimits\!\left(x\right) for n=1(1)10, x=0.01(.01)5 to 7D.

  • Zhang and Jin (1996, Table 19.1) tabulates \mathop{E_{{n}}\/}\nolimits\!\left(x\right) 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.

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