"Convergents" Example Sentences
1. In mathematics, continued fractions are represented as a sequence of convergents.
2. The convergents of the Golden Ratio are particularly interesting.
3. John's research paper on the convergents of complex functions was well-received.
4. The sequence of convergents for pi is infinite.
5. The notion of convergents is useful in approximating irrational numbers.
6. The logarithmic continued fraction has remarkable properties related to its convergents.
7. The Handbook of Continued Fractions for Special Functions explores the relationship between Euler's constant and its convergents.
8. The exponential continued fraction is defined in terms of the convergents of the corresponding continued fraction.
9. The accuracy of convergents can be improved through the use of numerical algorithms.
10. The Pell equation is related to the convergents of the square root of 2.
11. The ratio of successive convergents of the continued fraction of an irrational number is a particularly interesting topic.
12. The continued fraction of a quadratic irrational has many useful properties related to its convergents.
13. The continued fraction of the square root of a prime has a periodic sequence of convergents.
14. The Chakravala method, which was used by ancient Indian mathematicians, was used to find the convergents of certain Diophantine equations.
15. Continued fractions play a crucial role in the study of Diophantine approximations, which are approximations of irrational numbers using convergents of their continued fractions.
16. The convergents of the Jacobi theta functions are related to the modular forms of weight 1.
17. The Leibniz formula for pi is based on the arctangent function and its series of convergents.
18. The Rabotnov continued fraction has a unique sequence of convergents that is connected to the theory of continued fractions.
19. The continued fraction for e has a sequence of convergents that is related to the Euler numbers.
20. The convergents of the Legendre elliptic integrals are important tools for solving transcendental equations related to elliptic functions.
21. The universal continued fraction has a unique sequence of convergents related to its coefficients.
22. The generalized continued fraction is defined by a sequence of convergents for a given function.
23. The modular continued fraction has a sequence of convergents that is related to the Dedekind eta function.
24. The properties of the continued fraction of the Euler-Mascheroni constant depend on the sequence of its partial convergents.
25. In cryptography, the convergents of continued fractions are used to encrypt messages.
26. The extended continued fraction expansions have a sequence of convergents associated with them.
27. The Gauss continued fraction has a sequence of convergents that are important for solving certain types of quadratic equations.
28. The convergents of the Apéry's constant are related to the Riemann zeta function.
29. The Padé approximations are defined in terms of the convergents of the corresponding continued fractions.
30. The convergents of the alternating harmonic series are related to the Basel problem.
Common Phases
1. The
convergents of the sequence;
2.
Convergents of the continued fraction;
3.
Convergents of the infinite series;
4.
Convergents of the polynomial expression;
5.
Convergents of the recursive function.