Lemniscate elliptic functionsIn mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied by Giulio Fagnano in 1718 and later by Leonhard Euler and Carl Friedrich Gauss, among others. The lemniscate sine and lemniscate cosine functions, usually written with the symbols sl and cl (sometimes the symbols sinlem and coslem or sin lemn and cos lemn are used instead), are analogous to the trigonometric functions sine and cosine.
Hyperbolic functionsIn mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola. Also, similarly to how the derivatives of sin(t) and cos(t) are cos(t) and –sin(t) respectively, the derivatives of sinh(t) and cosh(t) are cosh(t) and +sinh(t) respectively. Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry.
Even and odd functionsIn mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series. They are named for the parity of the powers of the power functions which satisfy each condition: the function is an even function if n is an even integer, and it is an odd function if n is an odd integer.
Inverse trigonometric functionsIn mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.
Hokkuis the opening stanza of a Japanese orthodox collaborative linked poem, renga, or of its later derivative, renku (haikai no renga). From the time of Matsuo Bashō (1644–1694), the hokku began to appear as an independent poem, and was also incorporated in haibun (in combination with prose). In the late 19th century, Masaoka Shiki (1867–1902) renamed the standalone hokku as "haiku", and the latter term is now generally applied retrospectively to all hokku appearing independently of renku or renga, irrespective of when they were written.
For loopIn computer science a for-loop or for loop is a control flow statement for specifying iteration. Specifically, a for loop functions by running a section of code repeatedly until a certain condition has been satisfied. For-loops have two parts: a header and a body. The header defines the iteration and the body is the code that is executed once per iteration. The header often declares an explicit loop counter or loop variable. This allows the body to know which iteration is being executed.
Bessel functionBessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions y(x) of Bessel's differential equation for an arbitrary complex number , which represents the order of the Bessel function. Although and produce the same differential equation, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of . The most important cases are when is an integer or half-integer.
RengaRenga (連歌, linked poem) is a genre of Japanese collaborative poetry in which alternating stanzas, or ku (句), of 5-7-5 and 7-7 mora (sound units, not to be confused with syllables) per line are linked in succession by multiple poets. Known as tsukuba no michi (筑波の道 The Way of Tsukuba) after the famous Tsukuba Mountain in the Kantō region, the form of poetry is said to have originated in a two-verse poetry exchange by Yamato Takeru and later gave birth to the genres haikai (俳諧) and haiku (俳句).
Kirejiare a special category of words used in certain types of Japanese traditional poetry. It is regarded as a requirement in traditional haiku, as well as in the hokku, or opening verse, of both classical renga and its derivative renku (haikai no renga). There is no exact equivalent of kireji in English, and its function can be difficult to define. It is said to supply structural support to the verse. When placed at the end of a verse, it provides a dignified ending, concluding the verse with a heightened sense of closure.
Conditional (computer programming)In computer science, conditionals (that is, conditional statements, conditional expressions and conditional constructs) are programming language commands for handling decisions. Specifically, conditionals perform different computations or actions depending on whether a programmer-defined Boolean condition evaluates to true or false. In terms of control flow, the decision is always achieved by selectively altering the control flow based on some condition (apart from the case of branch predication).
HaikuHaiku is a type of short form poetry that originated in Japan. Traditional Japanese haiku consist of three phrases composed of 17 phonetic units (called on in Japanese, which are similar to syllables) in a 5, 7, 5 pattern; that include a kireji, or "cutting word"; and a kigo, or seasonal reference. Similar poems that do not adhere to these rules are generally classified as senryū. Haiku originated as an opening part of a larger Japanese poem called renga.
Weierstrass elliptic functionIn mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions are also referred to as ℘-functions and they are usually denoted by the symbol ℘, a uniquely fancy script p. They play an important role in the theory of elliptic functions. A ℘-function together with its derivative can be used to parameterize elliptic curves and they generate the field of elliptic functions with respect to a given period lattice.
