strictly monotonic
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11: 21.1 Special Notation
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positive integers. | |
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complex, symmetric matrix with strictly positive definite, i.e., a Riemann matrix. | |
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12: 18.16 Zeros
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►Then is strictly increasing in and strictly decreasing in ; furthermore, if , then is strictly increasing in .
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13: 8.13 Zeros
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►The negative zero decreases monotonically in the interval , and satisfies
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14: 9.8 Modulus and Phase
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§9.8(iii) Monotonicity
…15: 26.9 Integer Partitions: Restricted Number and Part Size
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►equivalently, partitions into at most parts either have exactly parts, in which case we can subtract one from each part, or they have strictly fewer than parts.
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16: 8.3 Graphics
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►Some monotonicity properties of and in the four quadrants of the ()-plane in Figure 8.3.6 are given in Erdélyi et al. (1953b, §9.6).
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17: 18.36 Miscellaneous Polynomials
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►For the Laguerre polynomials this requires, omitting all strictly positive factors,
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18: 22.20 Methods of Computation
19: 3.8 Nonlinear Equations
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(b)
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and , do not change sign between and (monotonic convergence).
, , do not change sign in the interval , and (monotonic convergence after the first iteration).
20: 1.11 Zeros of Polynomials
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►with real coefficients, is called stable if the real parts of all the zeros are strictly negative.
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