# Addition theorem

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## Explanation

**Addition theorem**: In mathematics, an addition theorem is a formula such as that for the exponential function e = e·e that expresses, for a particular function f, f in terms of f and f. Slightly more generally, as is the case with the trigonometric functions sin and cos, several functions may be involved; this is more apparent than real, in that case, since there cos is an algebraic function of sin.

## Printed dictionaries and other books with definitions for Addition theorem

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### An Exploration of Dynamical Systems and Chaos (2015)

Completely Revised and Enlarged Second Edition by John Argyris, Gunter Faust, Maria Haase, Rudolf Friedrich

• **Addition theorem** for arbitrary
events (formula of Sylvester): The summation rule is valid for disjoint events; * the
addition theorem is an extension to arbitrary, not necessarily disjoint events* (fig.

### Elements of Homotopy Theory (2012)

by George W. Whitehead

* The homotopy addition theorem is a formula relating the element j*.(x) with the
elements 3% = tr.:(x0), x1, ..., x, 1. It will be used in the proof of the Hurewicz
theorem, and it appears implicitly in obstruction theory in the fact that the
obstruction ...

### Mathematics and Its History (2004)

by John Stillwell

* An addition theorem is a formula expressing* /(«, + u2) in terms of /(«,) and f(u2),
and perhaps also f'(u}) and f'(u2). For example,

**the addition theorem**for the sine function is sin(w, +w2) = sinw, Since the derivative, cosw, of sinw equals \/l -sin2w ...

### Applied Mathematics (2016)

by CTI Reviews

**Addition theorem**: In
mathematics, * an addition theorem is a formula such as that for the exponential
function ex + y =exˇey that expresses,foraparticular functionf, f intermsof f*(x) andf(
y) ...

### Weighing Goods (2017)

Equality, Uncertainty and Time by John Broome

The second premise of * the
interpersonal addition theorem is that the general betterness relation is coherent*.

### Nature (1920)

by Sir Norman Lockyer

=o-6 by using * the addition theorem is a method which seems
unnecessarily cumbrous*. P. 91, ex. 11. The equation are tan x: are sear—45°
seems to lead to a cubic equation. Methods for solving cubics are not given until
P- 144P ...

### The Philosopher's Dictionary - Third Edition (2002)

by Robert M. Martin

speech **addition theorem** 1' rule something. Some
philosophers think that there can be a moral difference between these even
when they have the same motives and outcome. For example, it has been argued
that an act ...

### The Dictionary of Psychology (2016)

by Ray Corsini

**addition theorem** A probability theorem to determine the
chances of a complex event occurring when occurrences of simple events are
known. additive ...

### CRC Concise Encyclopedia of Mathematics, Second Edition (2002)

by Eric W. Weisstein

See also CONDON-SHORTLEY PHASE, CORRELATION COEFFICIENT,
SECTORIAL HARMONIC, SOLID HARMONIC, SPHERICAL HARMONIC
**ADDITION THEOREM**, SPHERICAL HARMONIC DIFFERENTIAL EQUATION,
SPHERICAL ...

### Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (2003)

by I. Grattan-Guinness

The result was **the famous addition theorem**
for elliptic integrals, published in 1757, which expresses the general integral of
the differential equation as the 531 ELLIPTIC INTEGRALS AND FUNCTIONS.

### The VNR Concise Encyclopedia of Mathematics (2012)

by W. Gellert

Without using the x, y-system **the addition theorem** for the sine function can be
derived from that for the cosine function and the quadrant relations for arbitrary
angles: sin (2 + 6) = cos [t/2 – (or + 6)] = cos [(n/2 – c.) – 6] = cos (n/2 – c.) cos (–6)
...

### The Encyclopedia Americana (1905)

A universal reference library comprising the arts and sciences ... commerce, etc., of the world by George Edwin Rines, Frederick Converse Beach

=sin a cos (9 — cos a sin /9, are together
named **the Addition Theorem** for Sine and Cosine. Formula (1) is equivalent to
the preceding one; (2) results from (1) on replacing — BiorB; (3) from (1) on ...

### Dictionary of Material Science and High Energy Physics (2001)

by Dipak K. Basu

**addition theorem** The identity
, ...

### Encyclopaedia of Mathematics (set) (1994)

by Michiel Hazewinkel

**The
addition theorem** (which was formulated as a problem in [1]) was established in [
3] for ...

### Blackie’s Dictionary of Physics

by Blackie

Harmonic
Waves: From harmonic **addition theorem**, any superposition of harmonic waves ...

### Encyclopedia of Optimization (2001)

**The addition theorem** for expectation values and the symmetry of index choices
yield Conv(ai, . . . , an) is a facet intersected by Span(u, v) Here, one integrates
over all possible configurations of ai, . . . , am, u, v and weights with regard to the
...

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