## 8 Citations

### A Method to Reduce the Lehmer Measure in a Multi-Term Machin-Like Formula for π

- MathematicsOpen Journal of Applied Sciences
- 2022

Previously we have proposed a new method of transforming quotients into integer reciprocals in the Machin-like formulas for π . As a further development, here we show how to generate a multi-term…

### A new form of the Machin-like formula for pi by iteration with increasing integers

- Business, Mathematics
- 2021

This research work describes how to generate a new form of the Machin-like formula for pi by iteration with increasing integers.

### Algorithmic Determination of a Large Integer in the Two-Term Machin-like Formula for π

- MathematicsMathematics
- 2021

In our earlier publication we have shown how to compute by iteration a rational number u2,k in the two-term Machin-like formula for π of the kind π4=2k−1arctan1u1,k+arctan1u2,k,k∈Z,k≥1, where u1,k…

### Evaluating wider impacts of books via fine-grained mining on citation literatures

- Computer Science, EducationScientometrics
- 2020

Experimental results infer that citation literatures are a promising source for book impact assessment, especially books’ academic impacts, especially book’s academic impacts.

### Unconditional Applicability of Lehmer’s Measure to the Two-Term Machin-like Formula for π

- Mathematics
- 2020

Lehmer in his publication [6] defined a measure $$ \mu=\sum\limits_{j=1}^J\frac{1}{\log_{10}\left(\left|\beta_j\right|\right)}, $$ where $\beta_j$ is a set of the constants that may be either…

### Efficient computation of pi by the Newton - Raphson iteration and a two-term Machin-like formula

- Mathematics
- 2017

In our recent publication we have proposed a new methodology for determination of the two-term Machin-like formula for pi with small arguments of the arctangent function of kind $$ \frac{\pi }{4} =…

### An iteration procedure for a two-term Machin-like formula for pi with small Lehmer's measure

- Mathematics
- 2017

In this paper we present a two-term Machin-like formula for pi \[\frac{\pi}{4} = 2^{k - 1}\arctan\left(\frac{1}{u_1}\right) + \arctan\left(\frac{1}{u_2}\right)\] with small Lehmer's measure $e…

### The two-term Machin-like formula for pi with small arguments of the arctangent function

- Mathematics, Philosophy
- 2017

In this paper we propose a new method for determination of the two-term Machin-like formula for pi with arbitrarily small arguments of the arctangent function. This approach excludes irrational…

## References

SHOWING 1-2 OF 2 REFERENCES

### The Lebesgue Integral

- Mathematics
- 1951

Author's preface 1. Sets of points 2. Measure 3. The Lebesgue integral 4. Differentiation and integration 5. Further properties of the integral 6. The Lebesgue-Stieltjes integral Solutions of some…

### The Lebesgue Integral, (Cambridge tracts in mathematics and mathematical physics

- 1951