Bateman-type%20sums
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1: 18.18 Sums
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§18.18(vi) Bateman-Type Sums
►Jacobi
… ►§18.18(viii) Other Sums
… ►See also (18.38.3) for a finite sum of Jacobi polynomials. … ►2: 24.20 Tables
§24.20 Tables
►Abramowitz and Stegun (1964, Chapter 23) includes exact values of , , ; , , , , 20D; , , 18D. ►Wagstaff (1978) gives complete prime factorizations of and for and , respectively. …3: 20 Theta Functions
Chapter 20 Theta Functions
…4: 27.2 Functions
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►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes.
…It can be expressed as a sum over all primes :
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►the sum of the th powers of the positive integers that are relatively prime to .
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►is the sum of the th powers of the divisors of , where the exponent can be real or complex.
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►Table 27.2.2 tabulates the Euler totient function , the divisor function (), and the sum of the divisors (), for .
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5: 25.12 Polylogarithms
6: 4.27 Sums
§4.27 Sums
►For sums of trigonometric and inverse trigonometric functions see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §§14–42), Oberhettinger (1973), and Prudnikov et al. (1986a, Chapter 5).7: 6.16 Mathematical Applications
8: 26.3 Lattice Paths: Binomial Coefficients
9: 4.11 Sums
§4.11 Sums
…10: 26.10 Integer Partitions: Other Restrictions
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►where the last right-hand side is the sum over of the generating functions for partitions into distinct parts with largest part equal to .
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►where the inner sum is the sum of all positive odd divisors of .
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►where the sum is over nonnegative integer values of for which .
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►where the sum is over nonnegative integer values of for which .
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►where the inner sum is the sum of all positive divisors of that are in .
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