relation%20to%20Fuchsian%20equation
(0.004 seconds)
11—20 of 926 matching pages
11: 25.12 Polylogarithms
…
►The remainder of the equations in this subsection apply to principal branches.
…
►The special case is the Riemann zeta function: .
…
►Further properties include
…and
…
►In terms of polylogarithms
…
12: 28.2 Definitions and Basic Properties
…
►A solution with the pseudoperiodic property (28.2.14) is called a Floquet
solution with respect to
.
…Therefore a nontrivial solution is either a Floquet solution with respect to
, or is a Floquet solution with respect to
.
…
►leads to a Floquet solution.
…
►
§28.2(vi) Eigenfunctions
►Table 28.2.2 gives the notation for the eigenfunctions corresponding to the eigenvalues in Table 28.2.1. …13: 28.20 Definitions and Basic Properties
…
►
§28.20(ii) Solutions , , , ,
… ►Then from §2.7(ii) it is seen that equation (28.20.2) has independent and unique solutions that are asymptotic to as in the respective sectors , being an arbitrary small positive constant. …as with , and …as with . … ►§28.20(iv) Radial Mathieu Functions ,
…14: 20 Theta Functions
Chapter 20 Theta Functions
…15: Tom M. Apostol
…
►Apostol was born on August 20, 1923.
…
►He was also a coauthor of three textbooks written to accompany the physics telecourse The Mechanical Universe …and Beyond.
…
►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.
…
►
…
16: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
…
►
§26.4(i) Definitions
… ►It is also the number of -dimensional lattice paths from to . For , the multinomial coefficient is defined to be . … ►(The empty set is considered to have one permutation consisting of no cycles.) … ►§26.4(iii) Recurrence Relation
…17: 26.3 Lattice Paths: Binomial Coefficients
…
►
§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
…18: 27.2 Functions
…
►( 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.
…
►the sum of the th powers of the positive integers that are relatively prime to
.
…
►is the number of -tuples of integers whose greatest common divisor is relatively prime to
.
…