Fresnel integrals
(0.004 seconds)
11—20 of 32 matching pages
11: 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.
Zhang and Jin (1996, p. 642) includes the first 10 zeros of , 9D; the first 25 distinct zeros of and , 8S.
12: 7.14 Integrals
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§7.14(ii) Fresnel Integrals
►Laplace Transforms
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7.14.5
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7.14.6
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►In a series of ten papers Hadži (1968, 1969, 1970, 1972, 1973, 1975a, 1975b, 1976a, 1976b, 1978) gives many integrals containing error functions and Fresnel integrals, also in combination with the hypergeometric function, confluent hypergeometric functions, and generalized hypergeometric functions.
13: 7.11 Relations to Other Functions
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Confluent Hypergeometric Functions
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7.11.6
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Generalized Hypergeometric Functions
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7.11.7
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7.11.8
14: 7.24 Approximations
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§7.24(i) Approximations in Terms of Elementary Functions
… ►Cody (1969) provides minimax rational approximations for and . The maximum relative precision is about 20S.
Shepherd and Laframboise (1981) gives coefficients of Chebyshev series for on (22D).
Luke (1969b, vol. 2, pp. 422–435) gives main diagonal Padé approximations for , , , , and ; approximate errors are given for a selection of -values.
15: 7 Error Functions, Dawson’s and Fresnel Integrals
Chapter 7 Error Functions, Dawson’s and Fresnel Integrals
…16: 7.21 Physical Applications
§7.21 Physical Applications
►The error functions, Fresnel integrals, and related functions occur in a variety of physical applications. Fresnel integrals and Cornu’s spiral occurred originally in the analysis of the diffraction of light; see Born and Wolf (1999, §8.7). …17: 7.22 Methods of Computation
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§7.22(i) Main Functions
…18: Software Index
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7 Error Functions, Dawson’s and Fresnel Integrals | |||||||||||||||||||||||||
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7.25(iv) , , , , | ✓ | ✓ | ✓ | a | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ||||||||||
7.25(v) , , | ✓ | a | ✓ | ✓ | ✓ | ✓ | |||||||||||||||||||
7.25(vi) , , , , | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | |||||||||||||
7.25(vii) , , | ✓ | ✓ | ✓ | ||||||||||||||||||||||
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19: 7.10 Derivatives
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