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Gamma function

In mathematics, the gamma function is one used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For any positive integer n, Γ =!. Derived by Daniel Bernoulli, for complex numbers with a positive real part the gamma function is defined via a convergent improper integral: Γ = ∫ 0 ∞ x z − 1 e − x d x, ℜ > 0. The gamma function is defined as the analytic continuation of this integral function to a meromorphic function, holomorphic in the whole complex plane except the non-positive integers, where the function has simple poles; the gamma function has no zeroes, so the reciprocal gamma function 1 / Γ is an entire function. In fact, the gamma function corresponds to the Mellin transform of the negative exponential function: Γ =. Other extensions of the factorial function do exist, but the gamma function is the most popular and useful, it is a component in various probability-distribution functions, as such it is applicable in the fields of probability and statistics, as well as combinatorics.

The gamma function can be seen as a solution to the following interpolation problem: "Find a smooth curve that connects the points given by y =! at the positive integer values for x."A plot of the first few factorials makes clear that such a curve can be drawn, but it would be preferable to have a formula that describes the curve, in which the number of operations does not depend on the size of x. The simple formula for the factorial, x! = 1 × 2 × ⋯ × x, cannot be used directly for fractional values of x since it is only valid when x is a natural number. There are speaking, no such simple solutions for factorials. A good solution to this is the gamma function. There are infinitely many continuous extensions of the factorial to non-integers: infinitely many curves can be drawn through any set of isolated points; the gamma function is the most useful solution in practice, being analytic, it can be characterized in several ways. However, it is not the only analytic function which extends the factorial, as adding to it any analytic function, zero on the positive integers, such as k sin mπx, will give another function with that property.

A more restrictive property than satisfying the above interpolation is to satisfy the recurrence relation defining a translated version of the factorial function, f = 1, f = x f, for x equal to any positive real number. But this would allow for multiplication by any periodic analytic function which evaluates to one on the positive integers, such as ek sin mπx. There is a final way to solve this ambiguity: The Bohr–Mollerup theorem states that when the condition that f be logarithmically convex is added, it uniquely determines f for positive, real inputs. From there, the gamma function can be extended to all real and complex values by using the unique analytic continuation of f; the notation Γ is due to Legendre. If the real part of the complex number z is positive the integral Γ = ∫ 0 ∞ x z − 1 e − x d x converges and is known as the Euler integral of the second kind. Using integration by parts, one sees that: Γ = ∫ 0 ∞ x z e

Shin Panthagu

The Venerable Shin Panthagu was primate of Pagan Kingdom from 1115 to 1168. The Theravada Buddhist monk, son of the lord of Seinnyet, succeeded his teacher Shin Arahan as primate. For the next five decades, he was the chief religious adviser to King Alaungsithu, helped advise many of Alaungsithu's religious deeds; the notable works were the repairs of the Buddhagaya Temple circa 1118, the buildings of the Thatbyinnyu Temple, the Shwegugyi Temple. In 1168, he left Pagan for Ceylon in protest of Narathu who killed his father Alaungsithu and his elder brother Min Shin Saw to seize the throne. Shin Panthagu was disgusted by Narathu's treachery because Narathu used Panthagu in his scheme. By Narathu's urging, Shin Panthagu had gone and asked Min Shin Saw, whose troops were massed outside Pagan, to take the throne—with the explicit promise by Narathu that he would not harm Min Shin Saw. Narathu did not harm Min Shin Saw during their initial meet but poisoned his brother that night. Shin Panthagu returned to Pagan after Narapatisithu's accession to the throne in 1174.

Shin Uttarajiva, a renowned Mon monk who had studied in Ceylon, was the primate but Shin Panthagu was treated as the primate. The elderly Shin Panthagu died soon after. Harvey, G. E.. History of Burma: From the Earliest Times to 10 March 1824. London: Frank Cass & Co. Ltd

Jean Bouise

Jean Bouise was a French actor. He was born in Le Havre. In the 1950s he helped to found Théâtre de la Cité, was a player in the company, he entered films in the 1960s, played a supporting roles in The Shameless Old Lady, Z, L'Aveu, Out 1, The Return of the Tall Blond Man with One Black Shoe, Section spéciale, Monsieur Klein. He received César nominations for his roles in Le vieux fusil and Le Juge Fayard dit Le Shériff, before winning the Best Supporting Actor award for Coup de tête. Subsequently, he appeared in Édith et Marcel, Le Dernier Combat, The Big Blue and La Femme Nikita, he died in Lyon. Jean Bouise on IMDb

AlĂ­ Manouchehri

Alí Manuel Manouchehri Moghadam Kashan Lobos is a Chilean-Austrian football player. Professional football player with an outstanding experience in first class teams and internationally. Former National Team of Chile. Central Defender and Lateral. European Passport, his last club was Boyacá Chico, 1st Division of Colombia, where he was cataloged as "a warrior" and "The Lion" by the Colombian press, praised by the fans. Central defender both profiles, lateral. With experience in clubs of the first división in Chile, First B and internationally, he characterized by its power, its tactical football, dedication on the field. In the last season 2015–2016 he defended the colors of Union San Felipe, played 25 matches. With Ali as a defender, Union San Felipe was the team. Ali Manuchehri delivers experience: He debuted in 2005 with 17 years in Coquimbo Unido where he was sub champion in first división. Ali was the figure in the historic campaign of Coquimbo Unido, he score the winning goal against Everton in the minute 97.

In 2007, he played for Levante UD-B of Spain. In 2008, he played in First Division. In 2009, he played in Coquimbo Unido. In 2010, he played in First Division. In 2011, he played in first division. In 2012, he played in Deportes Concepción, where he was baptized by the people as "the Lion Manuchehri". In 2013–2014 he played in Coquimbo Unido, where he was champion of the Clausura championship of the First B. In 2015–2016, he played in Union San Felipe, he has been nominated to the Chilean nacional team. In the Chilean sub 23 national team In the adult Chilean national team He was awarded as the best defender of the international championship "FIF Pro" developed in Mexico. Ali Manuchehri has studied the career of professional coach, a supplement that enhances his work as a central defender. In 2016, he played in Boyacá Chicó FC, First Division, he was a member of the Chile national under-23 football team. Born to an Iranian father and a Chilean mother, Alí is eligible to play for the Iran national football team.

Web oficial Iranians to watch abroad: Ali Manouchehri – VIDEO Interview with Alí Manouchehri Alí Manouchehri, a half-Iranian player shining in Chile


A ploye is a Canadian flatbread type mix of buckwheat flour, wheat flour, baking powder and water, popular in the Madawaska region, Canada. First invented in Nova Scotia, they spread to the St. John Valley. Much like grits, or potatoes, the ploye was a simple carbohydrate filler food for the local population, it was cheap, easy to make, with local toppings, such as maple syrup or cretons, could vary in taste. This staple is eaten with baked beans. Over time however it became a traditional dish; the recipe is handed down through the generations. The batter itself is thin and runny so as to ensure it does not get too thick while cooking; the ploye resembles a crêpe in thickness. In Madawaska, the ployes have a yellow color due to the type of buckwheat used in the mixture. Recipes sometimes include a little vinegar to keep the cakes from turning red. A ploye, contrary to a pancake, is only cooked on one side. Once cooked, it is buttered, covered in maple syrup, brown sugar, molasses or cretons, it is rolled or folded up and eaten.

It is served with the local traditional chicken stew called fricot, which more resembles chicken soup with homemade flour dumplings. Ployes are served at local events and fairs, such as the Ployes Festival and Foire Brayonne. Kaletez List of buckwheat dishes Memil-buchimgae


Tall al-’Umayri is an archaeological dig site in western Jordan that dates back to The Early Bronze Age and extends forwards to the Hellenistic Period. It is located near the modern capital of Amman, is significant for its well preserved evidence of a Temple, as well as archaeological evidence of a network of small farms believed to produce wine. Excavations were proceeding as of 2014; the site sits atop a low ridge between the Queen Alia Airport highway and Amman National Park, c. 2900 feet above sea level. While the location offers few natural defenses, the location was selected to take advantage of a natural spring that flowed as as the 1930s according to local historian Raouf Abujaber, it appears that this would have been the only reliable water source for travelers between Amman and Madaba. The site was first noted by Charles Warren in 1867, but was not visited again by archaeologists until the Hisban regional survey in 1976, it has been the subject of several large-scale digs beginning in 1984 under the auspices of the Madaba Plains Project, which by 2010 had uncovered over 4,000 artifacts and 50,000 pieces of pottery.

Though the site appears never to havea had more than few dozen buildings, archaeological artifacts have been recovered from 21 different strata indicating that the site has been occupied for all but 1200 years since the early Bronze Age to the present, with a few flints and cherts from earlier. A dolmen from this earliest period contains disarticulated skeletons from at least 20 people, along with several associated structures and pottery fragments; this phase of occupation peaked c. 2500 BCE based on the ruins of several houses and streets, before declining to nothing by 2200 BCE. The site was recolonized and fortified with a 5m-deep moat topped by a 5m-tall rampart c. 1600 BCE, but there is no clear evidence it was occupied between 1550 and 1350 BCE. A large, well-preserved, five-room, two-story structure built in the Late Bronze Age has been the subject of some debate among archaeologists, it contained hundreds of unburnt animal bones, a cult-wall built around 5 natural standing stones, an Asherah figurine suggesting it was a temple.

Three substantial four room structures typical of the early Iron Age though predating them were built about a century and appear to have met a violent end. In addition to numerous kitchen and farmyard implements, the charred skeletons of four people and discarded weaponry were discovered within the ruins of the house. Occupation by a distinct culture begins again c. 1050 BCE, as inferred from a change in the pottery style. The evidence suggests a sparse population for the next four centuries. However, in c. 600 BCE a major administrative complex was built at'Umayri under the patronage of the Ammonite king Ba'alyasha' or Baalis, whose name was found on several seals from this stratum. Artifacts bearing a stamp with the word "'Ammon" written in Aramaic persist until c. 400 BCE, well into the Persian Era. After a two century hiatus, the site persisted as a farmstead built around the spring from 200 BCE to 135 CE. A tomb with a Greek inscription and a plastered ritual pool from the time period indicate connections to other Mediterranean cultures.

After 350 CE, numerous pottery fragments and wall fragments indicate it was at least transiently occupied during the Byzantine and Islamic periods, by the Bedouin into the 20th century. Jericho#Stone Age Madaba#Archaeological finds in Madaba city The Madaba Plains Project Database of artifacts on