User:Tea2min/Scratch

Older standards
R5RS and R6RS are already referenced from Scheme (programming language).
 * RRS ("The Revised Report on Scheme", G.L. Steele et al., AI Memo 452, MIT, Jan 1978)
 * R2RS ("The Revised Revised Report on the Algorithmic Language Scheme", Clinger, AI Memo 848, MIT Aug 1985)
 * R3RS ("Dedicated to the Memory of ALGOL 60", Revised(3) Report on the Algorithmic Language Scheme)
 * R4RS (Revised(4) Report on the Algorithmic Language Scheme)

History of

 * interaction with  (R5RS call/cc & dynamic-wind in terms of r4rs, faking dynamic-wind, dynamic-wind, A new specification for dynamic-wind, call/wc, and call/nwc, implementing dynamic-wind)
 * interaction with  and

Cosine powers
$$ (\cos\alpha)^n = \frac{1}{2^n}\sum_{k=0}^n\binom{n}{k}\cos((2k-n)\alpha) $$

$$ (\cos\alpha)^{2n} = \frac{1}{4^n}\left\{\binom{2n}{n} + 2\sum_{k=1}^n\binom{2n}{n-k}\cos(2k\alpha)\right\} $$

$$ (\cos\alpha)^{2n+1} = \frac{1}{4^n}\sum_{k=0}^n\binom{2n+1}{n-k}\cos((2k+1)\alpha) $$

Hermite polynomials
$$ H_{2n}(x) = (2n)!\ \sum_{k = 0}^n \frac{(-1)^{n - k}}{(2k)! (n - k)!} (2x)^{2k} $$

$$ H_{2n+1}(x) = (2n+1)!\ \sum_{k = 0}^n \frac{(-1)^{n - k}}{(2k + 1)! (n - k)!} (2x)^{2k + 1} $$

Persons with first name Hanan

 * Hanan al-Shaykh, a Lebanese author of contemporary Arab women's literature
 * Hanan Ashrawi, a Palestinian legislator, activist, and scholar
 * Hanan Habibzai, an Afghan journalist and writer
 * Hanan Qassab Hassan, a prominent Syrian writer and academic
 * Hanan Ahmed Khaled, an Egyptian female athlete
 * Hanan Porat, a former Israeli politician
 * Hanan Rubin, a German-born Israeli politician
 * Hanan Tork, an Egyptian actress and former ballerina

Semimathematics

 * Semicomputable function
 * Semi-continuity
 * Semi-deterministic Büchi automaton
 * Semi-differentiability
 * Semidirect product
 * Semi-elliptic operator
 * Semifield
 * Semigroup
 * Semigroup action
 * Semigroupoid
 * Semi-Hilbert space
 * Semi-implicit Euler method
 * Semi-infinite
 * Semi-infinite programming
 * Semilattice
 * Semi-local ring
 * Seminorm → Norm (mathematics)
 * Seminormal subgroup
 * Semiorder
 * Semiperfect number
 * Semiperfect ring
 * Semipermutable subgroup
 * Semiprime
 * Semiprime ring
 * Semiprimitive ring
 * Semiregular space
 * Semiring
 * Semi-s-cobordism
 * Semiset
 * Semisimple algebra
 * Semisimple algebraic group
 * Semisimple Lie algebra
 * Semisimple module
 * Semi-simple operator
 * Semistable abelian variety
 * Semi-Thue system

= Field of rational functions = In mathematics, given a field K, the field of rational functions K(X) is the field of all rational functions in the variable X with coefficients in K. It is the field of fractions of the polynomial ring K[X].

The field of rational functions is not to be confused with the field of rationals, which is the field of fractions for the ring of integers.

Given a field K, the ring K[X] of polynomials in the variable X with coefficients in K is an integral domain so that the field of fractions of K[X] can be constructed. K(X)/K is a field extension of infinite degree.