![]() | This template uses Lua: |
name | |
---|---|
[[File:{{{image}}}|frameless]] | |
Domain, codomain and image | |
Domain | domain |
Codomain | codomain |
Image | range |
Basic features | |
Parity | parity |
Period | period |
Specific values | |
At zero | zero |
Value at +∞ | plusinf |
Value at −∞ | minusinf |
Maxima | max |
Minima | min |
Value at vr1 | f1 |
Value at vr2 | f2 |
Value at [...] | [...] |
Value at vr5 | f5 |
Specific features | |
Asymptote | asymptote |
Root | root |
Critical point | critical |
Inflection point | inflection |
Fixed point | fixed |
notes |
{{Infobox mathematical function
| name =
| image= |imagesize= <!--(default 220px)--> |imagealt=
| parity= |domain= |codomain= |range= |period=
| zero= |plusinf= |minusinf= |max= |min=
| vr1= |f1= |vr2= |f2= |vr3= |f3= |vr4= |f4= |vr5= |f5=
| asymptote= |root= |critical= |inflection= |fixed=
| notes =
}}
The code below produces the box opposite:
Sine | |
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![]() | |
General information | |
General definition | |
Motivation of invention | Indian astronomy |
Date of solution | Gupta period |
Fields of application | Trigonometry, Integral transform, etc. |
Domain, codomain and image | |
Domain | (−∞, +∞) a |
Image | [−1, 1] a |
Basic features | |
Parity | odd |
Period | 2π |
Specific values | |
At zero | 0 |
Maxima | (2kπ + π/2, 1)b |
Minima | (2kπ − π/2, −1) |
Specific features | |
Root | kπ |
Critical point | kπ + π/2 |
Inflection point | kπ |
Fixed point | 0 |
Related functions | |
Reciprocal | Cosecant |
Inverse | Arcsine |
Derivative | |
Antiderivative | |
Other Related | cos, tan, csc, sec, cot |
Series definition | |
Taylor series | |
Generalized continued fraction | |
Gamma | |
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![]() The gamma function along part of the real axis | |
General information | |
General definition | , |
Deriver of General definition | Daniel Bernoulli |
Motivation of invention | Interpolation for factorial function |
Date of solution | 1720s |
Extends | Factorial function |
Fields of application | Probability, statistics, combinatorics |
Main applications | probability-distribution functions |
Domain, codomain and image | |
Domain | - ℤ0- |
Image | |
Basic features | |
Parity | Not even and not odd |
Period | No |
Analytic? | Yes |
Meromorphic? | Yes |
Holomorphic? | Yes except at ℤ0- |
Specific values | |
Maxima | No |
Minima | No |
Value at ℤ+ | |
Value at ℤ0- | Not defined |
Specific features | |
Root | No |
Critical point | ℤ0- |
Inflection point | ℤ0- |
Fixed point | 1 |
Poles | ℤ0- |
Transform | |
Corresponding transform | Mellin transform |
Corresponding transform formula |
{{Infobox mathematical function
| name = Sine
| image = Sinus.svg
| parity=odd |domain=(-∞,∞) |range=[-1,1] |period=2π
| zero=0 |plusinf= |minusinf= |max=((2k+½)π,1) |min=((2k-½)π,-1)
| asymptote= |root=kπ |critical=kπ-π/2 |inflection=kπ |fixed=0
| notes = Variable k is an [[integer]].
}}