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11—20 of 21 matching pages
11: 12.11 Zeros
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►For example, let the th real zeros of and , counted in descending order away from the point , be denoted by and , respectively.
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12: 1.10 Functions of a Complex Variable
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►If is the first negative integer (counting from ) with , then is a pole of order (or multiplicity) .
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►where and are respectively the numbers of zeros and poles, counting multiplicity, of within , and is the change in any continuous branch of as passes once around in the positive sense.
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►each location again being counted with multiplicity equal to that of the corresponding zero or pole.
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13: 18.21 Hahn Class: Interrelations
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14: DLMF Project News
error generating summary15: 1.2 Elementary Algebra
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►Thus is the product of the (counted according to their multiplicities) eigenvalues of .
…Thus is the sum of the (counted according to their multiplicities) eigenvalues of .
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16: Bibliography D
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Pólya’s Theory of Counting.
In Applied Combinatorial Mathematics, E. F. Beckenbach (Ed.),
pp. 144–184.
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17: 1.11 Zeros of Polynomials
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►A polynomial of degree with real or complex coefficients has exactly real or complex zeros counting multiplicity.
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18: 3.8 Nonlinear Equations
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►has zeros in , counting each zero according to its multiplicity.
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19: 26.12 Plane Partitions
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►Different configurations are counted as different plane partitions.
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20: 18.39 Applications in the Physical Sciences
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►Thus the two missing quantum numbers corresponding to EOP’s of order and of the type III Hermite EOP’s are offset in the node counts by the fact that all excited state eigenfunctions also have two missing real zeros.
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