Search results
Results from the WOW.Com Content Network
6.3 John transform. 7 Gauss's contiguous relations. ... The term "hypergeometric series" was first used by John Wallis in his 1655 book Arithmetica Infinitorum.
John Wallis (/ ˈ w ɒ l ɪ s /; [2] Latin: Wallisius; 3 December [O.S. 23 November] 1616 – 8 November [O.S. 28 October] 1703) was an English clergyman and mathematician, who is given partial credit for the development of infinitesimal calculus.
Wallis derived this infinite product using interpolation, though his method is not regarded as rigorous. A modern derivation can be found by examining ∫ 0 π sin n x d x {\displaystyle \int _{0}^{\pi }\sin ^{n}x\,dx} for even and odd values of n {\displaystyle n} , and noting that for large n {\displaystyle n} , increasing n ...
Their works on hyperbolic geometry had a considerable influence on its development among later European geometers, including Witelo, Gersonides, Alfonso, John Wallis and Saccheri. [8] In the 18th century, Johann Heinrich Lambert introduced the hyperbolic functions [9] and computed the area of a hyperbolic triangle. [10]
These recurrence relations are due to John Wallis (1616–1703) and Leonhard Euler (1707–1783). [14] These recurrence relations are simply a different notation for the relations obtained by Pietro Antonio Cataldi (1548-1626). As an example, consider the regular continued fraction in canonical form that represents the golden ratio φ:
The combination was achieved by John Wallis, Isaac Barrow, and James Gregory, the latter two proving predecessors to the second fundamental theorem of calculus around 1670. [ 23 ] [ 24 ] The product rule and chain rule , [ 25 ] the notions of higher derivatives and Taylor series , [ 26 ] and of analytic functions [ 27 ] were used by Isaac ...
The sequence () is decreasing and has positive terms. In fact, for all : >, because it is an integral of a non-negative continuous function which is not identically zero; + = + = () () >, again because the last integral is of a non-negative continuous function.
In the 17th century, the method of exhaustion led to the rectification by geometrical methods of several transcendental curves: the logarithmic spiral by Evangelista Torricelli in 1645 (some sources say John Wallis in the 1650s), the cycloid by Christopher Wren in 1658, and the catenary by Gottfried Leibniz in 1691.