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1: 7.18 Repeated Integrals of the Complementary Error Function
§7.18 Repeated Integrals of the Complementary Error Function
►§7.18(i) Definition
… ►§7.18(iii) Properties
… ► … ►Hermite Polynomials
…2: 29.10 Lamé Functions with Imaginary Periods
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►The first and the fourth functions have period ; the second and the third have period .
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29.10.2
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3: 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 . … ►The computation of these functions can be based on algorithms for the complementary error function with complex argument; compare (7.19.3). …4: 29.17 Other Solutions
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29.17.1
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►Lamé–Wangerin functions are solutions of (29.2.1) with the property that is bounded on the line segment from to .
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5: 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 .
►Alternative notations are , , , , , , , .
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6: 22.4 Periods, Poles, and Zeros
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►The other poles are at congruent points, which is the set of points obtained by making translations by , where .
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►Figure 22.4.1 illustrates the locations in the -plane of the poles and zeros of the three principal Jacobian functions in the rectangle with vertices , , , .
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►Figure 22.4.2 depicts the fundamental unit cell in the -plane, with vertices , , , .
The set of points , , comprise the lattice for the 12 Jacobian functions; all other lattice unit cells are generated by translation of the fundamental unit cell by , where again .
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►This half-period will be plus or minus a member of the triple ; the other two members of this triple are quarter periods of .
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