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11: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Tables Relating to Mathieu Functions: Characteristic Values, Coefficients, and Joining Factors.
2nd edition, National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C..
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Confluent hypergeometric equations and related solvable potentials in quantum mechanics.
J. Math. Phys. 41 (12), pp. 7964–7996.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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12: 25.12 Polylogarithms
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►The remainder of the equations in this subsection apply to principal branches.
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►The special case is the Riemann zeta function: .
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►Further properties include
…and
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►In terms of polylogarithms
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13: 20 Theta Functions
Chapter 20 Theta Functions
…14: 26.3 Lattice Paths: Binomial Coefficients
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§26.3(i) Definitions
► is the number of ways of choosing objects from a collection of distinct objects without regard to order. is the number of lattice paths from to . …The number of lattice paths from to , , that stay on or above the line is … ►§26.3(iii) Recurrence Relations
…15: Tom M. Apostol
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►Apostol was born on August 20, 1923.
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►He was also a coauthor of three textbooks written to accompany the physics telecourse The Mechanical Universe …and Beyond.
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►In 1998, the Mathematical Association of America (MAA) awarded him the annual Trevor Evans Award, presented to authors of an exceptional article that is accessible to undergraduates, for his piece entitled “What Is the Most Surprising Result in Mathematics?” (Answer: the prime number theorem).
… Ford Award, given to recognize authors of articles of expository excellence.
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16: 26.5 Lattice Paths: Catalan Numbers
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§26.5(i) Definitions
… ►It counts the number of lattice paths from to that stay on or above the line . … ►§26.5(iii) Recurrence Relations
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26.5.6
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26.5.7
17: 14 Legendre and Related Functions
Chapter 14 Legendre and Related Functions
…18: 27.2 Functions
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►( is defined to be 0.)
Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes.
…They tend to thin out among the large integers, but this thinning out is not completely regular.
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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 number of -tuples of integers whose greatest common divisor is relatively prime to
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19: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
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