conjugate
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11: 12.2 Differential Equations
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►Standard solutions are , , (not complex conjugate), for (12.2.2); for (12.2.3); for (12.2.4), where
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§12.2(vi) Solution ; Modulus and Phase Functions
►When is real the solution is defined by …unless , in which case is undefined. …Properties of follow immediately from those of via (12.2.21). …12: 26.1 Special Notation
13: 27.8 Dirichlet Characters
14: 10.11 Analytic Continuation
15: 18.23 Hahn Class: Generating Functions
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18.23.6
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16: 26.9 Integer Partitions: Restricted Number and Part Size
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►The conjugate partition is obtained by reflecting the Ferrers graph across the main diagonal or, equivalently, by representing each integer by a column of dots.
The conjugate to the example in Figure 26.9.1 is .
Conjugation establishes a one-to-one correspondence between partitions of into at most parts and partitions of into parts with largest part less than or equal to .
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17: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►A complex linear vector space is called an inner product space if an inner product
is defined for all with the properties: (i) is complex linear in ; (ii) ; (iii) ; (iv) if then .
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1.18.9
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1.18.18
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1.18.19
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►Also, because is real-valued, iff .
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18: 13.7 Asymptotic Expansions for Large Argument
19: 1.2 Elementary Algebra
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►the complex conjugate is
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1.2.29
►the Hermitian conjugate is
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1.2.30
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►If , , and are real the complex conjugate bars can be omitted in (1.2.40)–(1.2.42).
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