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1: 25.1 Special Notation
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►The main function treated in this chapter is the Riemann zeta function .
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►The main related functions are the Hurwitz zeta function , the dilogarithm , the polylogarithm (also known as Jonquière’s function ), Lerch’s transcendent , and the Dirichlet -functions .
nonnegative integers. | |
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complex variable. | |
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2: 35.4 Partitions and Zonal Polynomials
§35.4 Partitions and Zonal Polynomials
… ►For any partition , the zonal polynomial is defined by the properties … ►Normalization
… ►Orthogonal Invariance
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…3: 23.13 Zeros
4: 25.11 Hurwitz Zeta Function
§25.11 Hurwitz Zeta Function
►§25.11(i) Definition
… ►The Riemann zeta function is a special case: … ►
5: 10.58 Zeros
6: 9.9 Zeros
§9.9 Zeros
… ►They are denoted by , , , , respectively, arranged in ascending order of absolute value for … ►For error bounds for the asymptotic expansions of , , , and see Pittaluga and Sacripante (1991), and a conjecture given in Fabijonas and Olver (1999). … ► ► …7: 32.5 Integral Equations
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►Let be the solution of
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32.5.1
►where is a real constant, and is defined in §9.2.
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32.5.2
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32.5.3
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8: 4.14 Definitions and Periodicity
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4.14.7
►The functions and are entire.
In the zeros of are , ; the zeros of are , .
The functions , , , and are meromorphic, and the locations of their zeros and poles follow from (4.14.4) to (4.14.7).
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9: 4.28 Definitions and Periodicity
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4.28.2
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4.28.9
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4.28.12
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