About the Project

Pringsheim%20theorem

AdvancedHelp

(0.003 seconds)

1—10 of 198 matching pages

1: 1.12 Continued Fractions
Pringsheim’s Theorem
Van Vleck’s Theorem
2: 27.15 Chinese Remainder Theorem
§27.15 Chinese Remainder Theorem
This theorem is employed to increase efficiency in calculating with large numbers by making use of smaller numbers in most of the calculation. …Their product m has 20 digits, twice the number of digits in the data. By the Chinese remainder theorem each integer in the data can be uniquely represented by its residues (mod m 1 ), (mod m 2 ), (mod m 3 ), and (mod m 4 ), respectively. …These numbers, in turn, are combined by the Chinese remainder theorem to obtain the final result ( mod m ) , which is correct to 20 digits. …
3: 28.27 Addition Theorems
§28.27 Addition Theorems
Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. They are analogous to the addition theorems for Bessel functions (§10.23(ii)) and modified Bessel functions (§10.44(ii)). …
4: Peter L. Walker
Walker’s books are An Introduction to Complex Analysis, published by Hilger in 1974, The Theory of Fourier Series and Integrals, published by Wiley in 1986, Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and Examples and Theorems in Analysis, published by Springer in 2004. …
  • 5: 27.2 Functions
    §27.2(i) Definitions
    Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes. … (See Gauss (1863, Band II, pp. 437–477) and Legendre (1808, p. 394).) This result, first proved in Hadamard (1896) and de la Vallée Poussin (1896a, b), is known as the prime number theorem. … If ( a , n ) = 1 , then the Euler–Fermat theorem states that …
    6: 20 Theta Functions
    Chapter 20 Theta Functions
    7: Tom M. Apostol
    Apostol was born on August 20, 1923. … 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). …
    8: 30.10 Series and Integrals
    For an addition theorem, see Meixner and Schäfke (1954, p. 300) and King and Van Buren (1973). …
    9: 10.44 Sums
    §10.44(i) Multiplication Theorem
    §10.44(ii) Addition Theorems
    Neumann’s Addition Theorem
    Graf’s and Gegenbauer’s Addition Theorems
    10: 3.8 Nonlinear Equations
    Initial approximations to the zeros can often be found from asymptotic or other approximations to f ( z ) , or by application of the phase principle or Rouché’s theorem; see §1.10(iv). … …
    3.8.15 p ( x ) = ( x 1 ) ( x 2 ) ( x 20 )
    Consider x = 20 and j = 19 . We have p ( 20 ) = 19 ! and a 19 = 1 + 2 + + 20 = 210 . …