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.

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.

Isaac Newton performed experiments with light and prisms, presenting his findings in the Opticks ( 1704 ) that white light consists of several colours and that these colours cannot be decomposed any further.

As of 2010, the lineup consists of Seth Newton ( electric bass guitar, vocals ), Eric Trabucco ( electric guitar, vocals ), Paul Carter ( keys, vocals 2010-current ) and Brian Marcou ( drums, percussion ).

The North Newton government consists of a mayor and five council members.

The town consists of four districts, Earlestown, Wargrave, Vulcan Village and the original ancient Newton in Makerfield area, that makes up the eastern part of the town.

According to the Deep East Texas Council of Governments the region consists of the following twelve counties: Angelina, Houston, Jasper, Nacogdoches, Newton, Polk, Sabine, San Augustine, San Jacinto, Shelby, Trinity, and Tyler.

The Newton Park Campus is home to the majority of the student accommodation, which consists of eight halls.

The school consists of 6 main blocks Pascal ( Maths and English ), Eliot ( Geography, Art, ICT and RE ), Rousseau ( Modern foreign languages and History ), Ibsen ( Music and Drama ), Newton ( Science ) and Stephenson ( DT and Food Technology / Textiles ).

There are at least two Sears Homes in the old mill town of Newton Falls, New York, and the entire Town Site neighborhood in Bucksport, Maine, consists of Sears Homes in the Belfast model.

The band's line-up consists of Roddy Woomble ( lead vocals ), Rod Jones ( guitar, backing vocals ), Colin Newton ( drums ), Allan Stewart ( guitar ) and Gareth Russell ( bass ).

The electoral ward consists of the Caswell, Langland and Newton localities in the parliamentary constituency of Gower.

The parish consists of two large villages, Saint Paul Capesterre ( St. Paul's ) and Newton Ground, and their two subsidiary villages, Belmont Estate and Cranston Estate respectively.

The solar tidal acceleration at the Earth's surface was first given by Newton in the ' Principia '< ref >, Book 3, Proposition 36, Page 307 Newton put the force to depress the sea at places 90 degrees distant from the Sun at " 1 to 38604600 " ( in terms of g ), and wrote that the force to raise the sea along the Sun-Earth axis is " twice as great ", i. e. 2 to 38604600, which comes to about 0. 52 × 10 < sup >- 7 </ sup > g as expressed in the text .</ ref >

Although the two terms are used almost interchangeably, there is an important distinction: Wold Newton Family members-those who are descended from or otherwise related to the individuals exposed to the meteor strike ; and Wold Newton Universe members, unrelated to the family, who have met one or more family members in crossovers.

Newton operates under the Faulkner Act ( Council-Manager ) form of municipal government with a five-member Town Council, whose members are chosen in nonpartisan elections to four-year terms of office on a staggered basis, with two or three seats coming up for election in even years.

Cowper grew to be on such good terms with the Unwin family that he went to live in their house, and moved with them to Olney, where John Newton, a former slave trader who had repented and devoted his life to the gospel, was curate.

Following Newton, Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century explanations for gravity have usually been sought in terms of a field model, rather than a point attraction.

" This is a major departure from the approach of Newton, Einstein and Schrödinger, all of whom expressed their theories in terms of deterministic equations.

In 1687, Isaac Newton published Philosophiæ Naturalis Principia Mathematica, which provided an explanation for Kepler's laws in terms of universal gravitation and what came to be known as Newton's laws of motion.

And the very terms they use are scary, aren't they ?” Newton Maloney, Fuller Theological Seminary, Pasadena, California

The player is given a short document describing the life and notability of the historical person associated ( e. g. Isaac Newton ), but the document itself has some of its terms missing.

* He explains the mysterious drop in the value of the lunar acceleration parameter D " between the years AD 700-1300, which the American astrophycist Robert Newton had explained in terms of non-gravitational forces.

" This is a major departure from the approach of Newton, Einstein and Schrödinger, all of whom expressed their theories in terms of deterministic equations.

The letter must have convinced Newton of the sincerity of Montagu's good intentions towards him ; we find them living as friends on the most intimate terms until Halifax's death in 1715.

Following this, Newton then defined number, and the relationship between quantity and number, in the following terms: " By number we understand not so much a multitude of unities, as the abstracted ratio of any quantity to another quantity of the same kind, which we take for unity " ( Newton, 1728 ).

The Newton polygon is an effective device for understanding the leading terms

* In June, 2006, U. S. District Judge Robert W. Pratt ruled that a faith based-program called InnerChange at a Newton, Iowa prison, operated by Charles Colson's Prison Fellowship Ministries, unconstitutionally used tax money for a religious program that gave special privileges to inmates who accepted its evangelical Christian teachings and terms.

Unlike other PDAs being introduced at the same time, the Magic Cap system did not rely on handwriting recognition, which meant it was almost an afterthought in terms of media coverage when Apple introduced the Newton.

Douglas argues that since the real Mariane Pearl is what he terms a " bi-racial " woman an actress of similar heritage such as Thandie Newton should have had the role instead of a white actress.