Whipple theorem
(0.001 seconds)
21—30 of 126 matching pages
21: 27.2 Functions
…
►
§27.2(i) Definitions
… ►(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. …This is the number of positive integers that are relatively prime to ; is Euler’s totient. ►If , then the Euler–Fermat theorem states that …22: 5.5 Functional Relations
…
►
§5.5(iv) Bohr–Mollerup Theorem
…23: 19.15 Advantages of Symmetry
…
►Symmetry makes possible the reduction theorems of §19.29(i), permitting remarkable compression of tables of integrals while generalizing the interval of integration.
…These reduction theorems, unknown in the Legendre theory, allow symbolic integration without imposing conditions on the parameters and the limits of integration (see §19.29(ii)).
…
24: 23.23 Tables
…
►05, and in the case of the user may deduce values for complex by application of the addition theorem (23.10.1).
…
25: Bibliography W
…
►
Extension of a quadratic transformation due to Whipple with an application.
Adv. Difference Equ., pp. 2013:157, 8.
…
►
Some transformations of generalized hypergeometric series.
Proc. London Math. Soc. (2) 26 (2), pp. 257–272.
…
26: 27.11 Asymptotic Formulas: Partial Sums
…
►where , .
►Letting in (27.11.9) or in (27.11.11) we see that there are infinitely many primes if are coprime; this is Dirichlet’s theorem
on primes in arithmetic progressions.
…
►
27.11.15
►Each of (27.11.13)–(27.11.15) is equivalent to the prime number theorem (27.2.3).
The prime number theorem for
arithmetic progressions—an extension of (27.2.3) and first proved in de la Vallée Poussin (1896a, b)—states that if , then the number of primes with is asymptotic to as .
27: 27.12 Asymptotic Formulas: Primes
…
►
Prime Number Theorem
…28: 1.10 Functions of a Complex Variable
…
►
Picard’s Theorem
… ►§1.10(iv) Residue Theorem
… ►Rouché’s Theorem
… ►Lagrange Inversion Theorem
… ►Extended Inversion Theorem
…29: 1.4 Calculus of One Variable
…
►
Mean Value Theorem
… ►Fundamental Theorem of Calculus
… ►First Mean Value Theorem
… ►Second Mean Value Theorem
… ►§1.4(vi) Taylor’s Theorem for Real Variables
…30: 35.2 Laplace Transform
…
►