Essentially, Euler-MacLaurin summation can be applied whenever Carlson's theorem holds ; the Euler-MacLaurin formula is essentially a result obtaining from the study of finite differences and Newton series.

Other appearances include: John Hewson in The Soufflé Rises ( series 1 ); Pat Cash in The Desert Angel ; Cheryl Kernot in We Ain't Got Dames ( series 1 ); Bert Newton ; Amanda Keller and Anne Fulwood in This Night of Nights ( series 1 ); Glenn Ridge in Add Sex and Stir and Office Mole ( series 2 ); Glenn Robbins and Molly Meldrum in Add Sex and Stir, George Negus in Add Sex and Stir and Dick on the Line ( series 3 ) and Ian Baker-Finch in A Hole in the Heart.

* Newton, Ian ( 1973 ): Finches ( New Naturalist series ).

( Indirect proof via the inverse power series technique was given by Newton and Leibniz between 1670 and 1680.

However, a century later, Young and Fresnel revived the wave theory of light when they pointed out that light could be a transverse wave rather than a longitudinal wave — the polarization of a transverse wave ( like Newton's " sides " of light ) could explain birefringence, and in the wake of a series of experiments on diffraction the particle model of Newton was finally abandoned.

Starting around the 15th century, new algorithms based on infinite series revolutionized the computation of, and were used by mathematicians including Madhava of Sangamagrama, Isaac Newton, Leonhard Euler, Carl Friedrich Gauss, and Srinivasa Ramanujan.

The Newton series consists of the terms of the Newton forward difference equation, named after Isaac Newton ; in essence, it is the Newton interpolation formula, first published in his Principia Mathematica in 1687, namely the discrete analog of the continuum Taylor expansion,

Carlson's theorem provides necessary and sufficient conditions for a Newton series to be unique, if it exists.

However, a Newton series will not, in general, exist.

The Newton series, together with the Stirling series and the Selberg series, is a special case of the general difference series, all of which are defined in terms of suitably scaled forward differences.

The Newton platform was originally going to be programmed in the new Dylan programming language, but a lengthy series of delays combined with the " Not-Invented-Here syndrome " eventually led to it being abandoned.

Author Kim Newman has stated that his Anno Dracula series was partially inspired by the Wold Newton family.

The anthology series Tales of the Shadowmen edited by Jean-Marc Lofficier is also based on the Wold Newton concept and includes characters from French literature.

The juxtaposition of characters from different sources in the same story is similar to science fiction writer Philip José Farmer's works centering around the Wold Newton family or Kim Newman's Anno Dracula series.

It was decided that the protagonist of the new series would be the son of the earlier Tom Swift and his wife, Mary Nestor Swift ; the original hero continued as a series regular, as did his pal Ned Newton.

England contributed a young subaltern named Newton and the naval architect Samuel Bentham, brother to the economist, who for his colonel's commission was proving a godsend to the Russian fleet.

Meanwhile Newton ( 1642 – 1727 ) derived the relationship for wave velocity in solids, a cornerstone of physical acoustics ( Principia, 1687 ).

" Amazing Grace ", with the words written by Newton and joined with " New Britain ", the melody most currently associated with it, appeared for the first time in Walker's shape note tunebook Southern Harmony in 1847.

He sings the sixth and fifth verses in that order, and Stowe included another verse not written by Newton that had been passed down orally in African American communities for at least 50 years.

Newton also developed a law for the drag force on a flat plate inclined towards the direction of the fluid flow.

Newton was the first to develop a mathematical model for calculating the speed of sound, but it was not correct until Pierre-Simon Laplace accounted for the molecular behavior of gases and introduced the heat capacity ratio.

In his paper " The Application of Thought to Textual Criticism ," ( 1921 ) Housman stated: " A textual critic engaged upon his business is not at all like Newton investigating the motion of the planets: he is much more like a dog hunting for fleas.

In a 1973 revision of his compendium of essays, Profiles of the Future, Clarke acknowledged the Second Law and proposed the Third in order to round out the number, adding " As three laws were good enough for Newton, I have modestly decided to stop there ".

In just his second start, Newton threw for 432 yards against the defending Super Bowl Champion Green Bay Packers.

In their first match up of the 2011 season, Cam Newton set an NFL record for most rushing touchdowns in a season for QB with 13.

In their second match up of the 2011 season, Newton set the record for most passing yards in a season for a rookie QB and converted a 91 yard touchdown pass to WR Brandon LaFell to set a Carolina Panther records for longest pass.

The faculties of the Academy for Jewish Religion in New York and of the Rabbinical School of Hebrew College in Newton Centre, Massachusetts also includes a large number of Conservative rabbis.

Some sources, including Newton, refer to the entire force as a centripetal force, even for eccentric orbits, for which gravity is not aligned with the direction to the center of curvature.

At one point in its development it was intended for use with Apple's Newton computer, but the Dylan implementation did not reach sufficient maturity in time, and Newton instead used a combination of C and the NewtonScript developed by Walter Smith.

It was originally developed for the Apple Newton product.

In 1976 he earned acclaim for his first major film role, portraying Thomas Jerome Newton, an alien from a dying planet, in The Man Who Fell to Earth, directed by Nic Roeg.

To account for slowing due to friction, Leibniz theorized that thermal energy consisted of the random motion of the constituent parts of matter, a view shared by Isaac Newton, although it would be more than a century until this was generally accepted.

Abauzit is also notable for proofreading or correcting the writings of Isaac Newton and other scholars.

However, this policy was contentious among the encyclopedists and so some biographies were " hidden " inside articles ; for example, the article on Wolstrope ( Woolsthorpe ), England is almost entirely about the life of Newton.

He also came near to deducing that gravity follows an inverse square law, and that such a relation governs the motions of the planets, an idea which was subsequently developed by Newton.

The section from Alconbury to Water Newton, ignoring modern bypasses such as that at Stilton, follows the A1.

It follows the adventures of the mercenary Lawrence Newton as he attempts to capture what he believes is a fabulous treasure, only to find something of much greater importance.

The story follows the life of Lawrence Newton from the colony planet Amethi, both in the current time and in a series of flashbacks.

The second half of the book follows the lives of Eliza, Leibniz, Newton, Waterhouse, and Sophia Charlotte over the next 10 years.

The list of years that contain " Newton " week must be calculated by computer or obtained from a table or almanac, as it follows no simple rule.

Gwen storms out of the house in tears, and Newton follows her, thinking it is still part of the plan.

Although she resists, Newton follows her example and begins telling an outlandish romantic story of something they supposedly did, which makes Gwen decide to stay.

After introducing his diagram ' to find the force of the Sun to perturb the Moon ' in Book 3, Proposition 25, Newton developed a first approximation to the solar perturbing force, showing in further detail how its components vary as the Moon follows its monthly path around the Earth.

The series follows the personal and professional lives of one shift of police officers from the fictional Newton Park police station on Merseyside, England.