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arguments e±iπ/3

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11: 8.28 Software
§8.28(ii) Incomplete Gamma Functions for Real Argument and Parameter
§8.28(iii) Incomplete Gamma Functions for Complex Argument and Parameter
§8.28(iv) Incomplete Beta Functions for Real Argument and Parameters
§8.28(v) Incomplete Beta Functions for Complex Argument and Parameters
§8.28(vi) Generalized Exponential Integral for Real Argument and Integer Parameter
12: 35.10 Methods of Computation
§35.10 Methods of Computation
See Yan (1992) for the F 1 1 and F 1 2 functions of matrix argument in the case m = 2 , and Bingham et al. (1992) for Monte Carlo simulation on 𝐎 ( m ) applied to a generalization of the integral (35.5.8). …
13: 35 Functions of Matrix Argument
Chapter 35 Functions of Matrix Argument
14: 10.40 Asymptotic Expansions for Large Argument
§10.40 Asymptotic Expansions for Large Argument
Products
§10.40(ii) Error Bounds for Real Argument and Order
§10.40(iii) Error Bounds for Complex Argument and Order
15: 20.16 Software
§20.16(ii) Real Argument and Parameter
§20.16(iii) Complex Argument and/or Parameter
16: 22.22 Software
§22.22(ii) Real Argument
§22.22(iii) Complex Argument
17: 6.1 Special Notation
Unless otherwise noted, primes indicate derivatives with respect to the argument. The main functions treated in this chapter are the exponential integrals Ei ( x ) , E 1 ( z ) , and Ein ( z ) ; the logarithmic integral li ( x ) ; the sine integrals Si ( z ) and si ( z ) ; the cosine integrals Ci ( z ) and Cin ( z ) . …
18: 10.17 Asymptotic Expansions for Large Argument
§10.17 Asymptotic Expansions for Large Argument
§10.17(ii) Asymptotic Expansions of Derivatives
§10.17(iii) Error Bounds for Real Argument and Order
§10.17(iv) Error Bounds for Complex Argument and Order
§10.17(v) Exponentially-Improved Expansions
19: Software Index
20: 15.19 Methods of Computation
For z it is always possible to apply one of the linear transformations in §15.8(i) in such a way that the hypergeometric function is expressed in terms of hypergeometric functions with an argument in the interval [ 0 , 1 2 ] . For z it is possible to use the linear transformations in such a way that the new arguments lie within the unit circle, except when z = e ± π i / 3 . This is because the linear transformations map the pair { e π i / 3 , e π i / 3 } onto itself. However, by appropriate choice of the constant z 0 in (15.15.1) we can obtain an infinite series that converges on a disk containing z = e ± π i / 3 . …