arguments e±iπ/3
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11—20 of 539 matching pages
11: 8.28 Software
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§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 and functions of matrix argument in the case , and Bingham et al. (1992) for Monte Carlo simulation on 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
16: 22.22 Software
17: 6.1 Special Notation
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►Unless otherwise noted, primes indicate derivatives with respect to the argument.
►The main functions treated in this chapter are the exponential integrals , , and ; the logarithmic integral ; the sine integrals and ; the cosine integrals and .
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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
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Open Source | With Book | Commercial | |||||||||||||||||||||||
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16.27(ii) Real Arguments | ✓ | ✓ | ✓ | ✓ | a | ✓ | ✓ | ✓ | ✓ | ||||||||||||||||
16.27(iii) Complex Arguments | ✓ | a | ✓ | ✓ | ✓ | ✓ | |||||||||||||||||||
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22.22(ii) Real Argument | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||||||||
22.22(iii) Complex Argument | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | a | ✓ | |||||||||||||||
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23.24(ii) Real Argument | ✓ | ✓ | a | ||||||||||||||||||||||
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20: 15.19 Methods of Computation
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►For 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 .
►For it is possible to use the linear transformations in such a way that the new arguments lie within the unit circle, except when .
This is because the linear transformations map the pair onto itself.
However, by appropriate choice of the constant in (15.15.1) we can obtain an infinite series that converges on a disk containing .
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