path integral
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1: 20.13 Physical Applications
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►In the singular limit , the functions , , become integral kernels of Feynman path integrals (distribution-valued Green’s functions); see Schulman (1981, pp. 194–195).
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2: 1.6 Vectors and Vector-Valued Functions
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§1.6(iv) Path and Line Integrals
… ►then the length of a path for is …The path integral of a continuous function is …3: 5.21 Methods of Computation
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►Another approach is to apply numerical quadrature (§3.5) to the integral (5.9.2), using paths of steepest descent for the contour.
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4: 6.12 Asymptotic Expansions
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§6.12(i) Exponential and Logarithmic Integrals
… ►For the function see §9.7(i). … ►§6.12(ii) Sine and Cosine Integrals
… ► … ►5: Bibliography T
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Steepest descent paths for integrals defining the modified Bessel functions of imaginary order.
Methods Appl. Anal. 1 (1), pp. 14–24.
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6: 11.6 Asymptotic Expansions
7: 7.12 Asymptotic Expansions
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§7.12(ii) Fresnel Integrals
►The asymptotic expansions of and are given by (7.5.3), (7.5.4), and … ►They are bounded by times the first neglected terms when . … ►§7.12(iii) Goodwin–Staton Integral
►See Olver (1997b, p. 115) for an expansion of with bounds for the remainder for real and complex values of .8: 9.17 Methods of Computation
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►In the first method the integration path for the contour integral (9.5.4) is deformed to coincide with paths of steepest descent (§2.4(iv)).
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9: 6.2 Definitions and Interrelations
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§6.2(i) Exponential and Logarithmic Integrals
… ►where the path does not cross the negative real axis or pass through the origin. … ►§6.2(ii) Sine and Cosine Integrals
… ►where the path does not cross the negative real axis or pass through the origin. … …10: 16.17 Definition
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