principal value (or branch)
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11—20 of 158 matching pages
11: 12.1 Special Notation
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►Unless otherwise noted, primes indicate derivatives with respect to the variable, and fractional powers take their principal values.
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12: 4.3 Graphics
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►Figure 4.3.2 illustrates the conformal mapping of the strip onto the whole -plane cut along the negative real axis, where and (principal value).
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13: 14.25 Integral Representations
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►The principal values of and (§14.21(i)) are given by
…where the multivalued functions have their principal values when and are continuous in .
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14: 4.1 Special Notation
15: 14.21 Definitions and Basic Properties
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►When is complex , , and are defined by (14.3.6)–(14.3.10) with replaced by : the principal branches are obtained by taking the principal values of all the multivalued functions appearing in these representations when , and by continuity elsewhere in the -plane with a cut along the interval ; compare §4.2(i).
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16: 1.14 Integral Transforms
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1.14.3
►where the last integral denotes the Cauchy principal value (1.4.25).
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1.14.41
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1.14.44
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17: 6.3 Graphics
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18: 8.2 Definitions and Basic Properties
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8.2.2
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►However, when the integration paths do not cross the negative real axis, and in the case of (8.2.2) exclude the origin, and take their principal values; compare §4.2(i).
Except where indicated otherwise in the DLMF these principal values are assumed.
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