repeated integrals of
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1: 7.18 Repeated Integrals of the Complementary Error Function
2: 7.22 Methods of Computation
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§7.22(iii) Repeated Integrals of the Complementary Error Function
►The recursion scheme given by (7.18.1) and (7.18.7) can be used for computing . …3: 7.25 Software
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§7.25(ii) , , ,
…4: 7.21 Physical Applications
§7.21 Physical Applications
… ►Carslaw and Jaeger (1959) gives many applications and points out the importance of the repeated integrals of the complementary error function . …5: 7.23 Tables
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Abramowitz and Stegun (1964, Chapter 7) includes , , , 10D; , , 8S; , , 7D; , , , 6S; , , 10D; , , 9D; , , , 7D; , , , , 15D.
Zhang and Jin (1996, pp. 637, 639) includes , , , 8D; , , , 8D.
6: 7.1 Special Notation
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►The main functions treated in this chapter are the error function ; the complementary error functions and ; Dawson’s integral
; the Fresnel integrals
, , and ; the Goodwin–Staton integral
; the repeated integrals of the complementary error function ; the Voigt functions and .
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7: 12.7 Relations to Other Functions
8: Software Index
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Open Source | With Book | Commercial | |||||||||||||||||||||||
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7.25(ii) , , , | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | NMS | |||
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9: 9.10 Integrals
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§9.10(viii) Repeated Integrals
…10: Bibliography G
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Evaluation of the repeated integrals of the coerror function.
ACM Trans. Math. Software 3, pp. 240–252.
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Algorithm 521: Repeated integrals of the coerror function.
ACM Trans. Math. Software 3, pp. 301–302.
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Recursive computation of the repeated integrals of the error function.
Math. Comp. 15 (75), pp. 227–232.
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Algorithm 957: evaluation of the repeated integral of the coerror function by half-range Gauss-Hermite quadrature.
ACM Trans. Math. Softw. 42 (1), pp. 9:1–9:10.
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