Manuals/calci/tan

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TRIAL PAGE

For example TAN(1..100) can give an array of the results, which is the TAN value for each of the elements in the array. The array could be of any shape.

Failed to parse (syntax error): {\displaystyle f(x,r1,r2)=\Gamma[(r1+r2)/2](r1/r2)^r1/2*(x)r1/2-1/ Γ(r1/2)Γ(r2/2)(1+r1x/r2)^(r1+r2)/2, ==Description== <math>F(x,\lambda)=\begin{cases} 1-e^{-\lambda x} &, x \ge 0 \\ 0 &, x<0 \end{cases}}

Failed to parse (syntax error): {\displaystyle {\frac{n(n+1)}{(n-1)(n-2)(n-3)}*\frac{\sum{\frac{(xi-\bar{x})^4}{s}}\frac{-3(n-1)^2}{(n-2)(n-3)}}

${\frac {n(n+1)}{(n-1)(n-2)(n-3)}}{\frac {\sum (xi-{\bar {x}})^{4}}{s}}-{\frac {3(n-1)^{2}}{(n-2)(n-3)}}$

${\frac {\sum (xi-{\bar {x}})^{4}}{s}}$

${\frac {-3(n-1)^{2}}{(n-2)(n-3)}}$

Examples

1. Example 1

Spreadsheet

	A	B	C	D	E
1	2	3	7	9	15
2	8	12	13	20	25
3	14	3	9	6	15
4	12	23	1	42	17
5	11	20	9	78	25

From the above table values:

=MMULT(3,A1:A3)

15

21

24

=MMULT(6,A4:C4)

24

-30

54

1. Example 2

Matrix A

7	5
2	3
6	0
9	8

Matrix B

8	-4	11
2	7	5

• Here Matrix A is of order 4x2 and Matrix B is of order 2x3.
• So the Product Matrix is of order 4x3. i.e

1st Row 7*8+5*2 = 66  ;  7*(-4)+5*7 = 7  ;  7*11+5*5 = 102
2nd Row 2*8+3*2 = 22  ;  2*(-4)+3*7 = 13  ;  2*11+3*5 = 37 and so on

• =MMULT(B2:C5,D2:F3) gives

Result Matrix

66	7	102
22	13	37
48	-24	66
88	20	139

${\frac {{\binom {m}{x}}{\binom {N-M}{n-x}}}{\binom {m}{x}}}$

trial

Failed to parse (syntax error): {\displaystyle F(x,\mu,σ)=\frac{1}{2} \left[1+ erf \left (\frac{ln(x)-μ)}{σ\sqrt{2}}\right)\right ]= φ\left[\frac{ln(x)-μ}{σ}\right ]}

$F(x,\mu ,\sigma )={\frac {1}{2}}\left[1+erf\left({\frac {ln(x)-\mu )}{\sigma {\sqrt {2}}}}\right)\right]=\varphi \left[{\frac {ln(x)-\mu }{\sigma }}\right]$

\begin{bmatrix} a & b \\ c & d \\ \end{bmatrix}

Then |A|=a|e f -b|d f +c|d e

          h   i|       g    i|        g    h|

$a{\begin{vmatrix}e&f\\h&i\end{vmatrix}}-b{\begin{vmatrix}d&f\\g&i\end{vmatrix}}+c{\begin{vmatrix}d&e\\g&h\end{vmatrix}}$

Trial 2

Failed to parse (syntax error): {\displaystyle f(x,r1,r2)=Γ[(r1+r2)/2](r1/r2)^{r1/2}*(x)^{r1/2-1}/ Γ(r1/2)Γ(r2/2)(1+r1x/r2)^(r1+r2)/2}

$f(x,r1,r2)={\frac {\Gamma [{\frac {r1+r2}{2}}]({\frac {r1}{r2}})^{\frac {r1}{2}}}{\Gamma ({\frac {r1}{2}})\Gamma ({\frac {r2}{2}})}}*{\frac {(x)^{{\frac {r1}{2}}-1}}{({\frac {1+r1x}{r2}})^{\frac {r1+r2}{2}}}}$

$f(x,r_{1},r_{2})={\frac {\Gamma [{\frac {r_{1}+r_{2}}{2}}]({\frac {r_{1}}{r_{2}}})^{\tfrac {r_{1}}{2}}}{\Gamma ({\frac {r_{1}}{2}})\Gamma ({\frac {r_{2}}{2}})}}*{\frac {(x)^{{\tfrac {r_{1}}{2}}-1}}{({\frac {1+r_{1}x}{r_{2}}})^{\tfrac {r_{1}+r_{2}}{2}}}}$

trial

1..10@DSIN

v11031	DSIN
1	0.01745240643728351
2	0.03489949670250097
3	0.05233595624294383
4	0.0697564737441253
5	0.08715574274765817
6	0.10452846326765346
7	0.12186934340514748
8	0.13917310096006544
9	0.15643446504023087
10	0.17364817766693033

TRIAL3

$s_{x1}.s_{x2}={\sqrt {{\frac {1}{2}}(s_{x1}^{2}+s_{x2}^{2})}}$

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. TeX parse error: Double subscripts: use braces to clarify"): {\displaystyle s_{x}_{1}} $F(x,\alpha ,\beta )=1-e^{-}{({\frac {x}{\beta }})}^{\alpha }$

$P(x)={\begin{cases}0&for&x<a\\1/b-a&for&a<x<b\\0&for&x>b\end{cases}}$

$f(n)={\begin{cases}n/2,&{\mbox{if }}n{\mbox{ is even}}\\3n+1,&{\mbox{if }}n{\mbox{ is odd}}\end{cases}}$

${\begin{bmatrix}a_{11}&A_{21}^{T}\\A_{21}&A_{22}\end{bmatrix}}={\begin{bmatrix}l_{11}&0\\L_{21}&L_{22}\end{bmatrix}}{\begin{bmatrix}l_{11}&L_{21}^{T}\\0&L_{22}^{T}\end{bmatrix}}={\begin{bmatrix}l_{11}^{2}&L_{11}L_{21}^{T}\\L_{11}L_{21}&L_{21}L_{21}^{T}+L_{22}L_{22}^{T}\end{bmatrix}}$

Description

• This function gives the probability of the uniform distribution.
• Uniform distribution is a symmetric probability distribution.
• It is also called rectangular distribution.
• In $UNIFORMDISTRIBUTED(x,ll,ul)$ ,$x$ is the numeric value to find the probability of the distribution, $ll$ is the lower limit value and $ul$ is the upper limit value.
• The probability density function of the uniform distribution in the interval [a,b] are :

$P(x)={\begin{cases}0&for&x<a\\1/b-a&for&a<x<b\\0&for&x>b\end{cases}}$

Video

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Video1

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Trial 5

$\left[{\frac {redemption}{\left(1+{\frac {yld}{frequency}}\right)^{\left(N-1+{\frac {DSC}{E}}\right)}}}\right]+\left[{\dfrac {100*{\frac {rate}{frequency}}*{\frac {DFC}{E}}}{\left(1+{\dfrac {yld}{frequency}}\right)^{\left({\dfrac {DSC}{E}}\right)}}}\right]+\left[\sum _{k=2}^{N}{\dfrac {100*{\frac {rate}{frequency}}}{\left(1+{\dfrac {yld}{frequency}}\right)^{\left(k-1+{\dfrac {DSC}{E}}\right)}}}\right]-\left[100*{\frac {rate}{frequency}}*{\frac {A}{E}}\right]$

Another Equation

$\left[{\frac {redemption}{\left(1+{\frac {yld}{frequency}}\right)^{\left(N+N_{3}+{\frac {DSC}{E}}\right)}}}\right]+\left[{\dfrac {100*{\frac {rate}{frequency}}*\sum _{i=1}^{NC}{\dfrac {DC_{i}}{NL_{i}}}}{\left(1+{\dfrac {yld}{frequency}}\right)^{\left(N_{3}+{\frac {DSC}{E}}\right)}}}\right]+\left[\sum _{k=1}^{N}{\dfrac {100*{\frac {rate}{frequency}}}{\left(1+{\dfrac {yld}{frequency}}\right)^{\left(k-N_{2}+{\dfrac {DSC}{E}}\right)}}}\right]-\left[100*{\frac {rate}{frequency}}*\sum _{i=1}^{NC}{\frac {A_{i}}{NL_{i}}}\right]$

Trial 6

$\left[{\dfrac {\left(redemption+\left(\left(\sum _{i=1}^{NC}{\frac {DC_{i}}{NL_{i}}}\right)*{\frac {100*rate}{frequency}}\right)\right)-\left(par+\left(\left(\sum _{i=1}^{NC}{\frac {A_{i}}{NL_{i}}}\right)*{\frac {100*rate}{frequency}}\right)\right)}{par+\left(\left(\sum _{i=1}^{NC}{\frac {A_{i}}{NL_{i}}}\right)*{\frac {100*rate}{frequency}}\right)}}\right]*\left[{\frac {frequency}{\left(\sum _{i=1}^{NC}{\frac {DSC_{i}}{NL_{i}}}\right)}}\right]$

$f(x,\mu ,\sigma )={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{\frac {-(x-\mu )^{2}}{2\sigma ^{2}}}$

Trial

$\int \limits _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx$

${\frac {1}{\Gamma (s)}}\int \limits _{0}^{\infty }{\frac {x^{s-1}}{e^{x-1}}}\,dx$

1	2	3	4
5 6 7 5 6 7
	0	0	0
5 6 7 5 6 7
	0	0	0

DOC

Functions	Parameters
$
$$
$$$
$$F
$A
$C
$CELLS
$R
$X
$_
$d
$diag
$dth
$x
X$
ZJSON
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ac
accumulate
accumulatewith
across
add
addcolumn
addrow
addsequence
adjoint
aggregate
any
appendfunction
ar
async
atindex
atnode
backward
bindcolumn
branch
branchvalues
c
calci
car
cartesianproduct
cdr
cell
cells
checktype
chunks
ci
clean
clear
clearcopy
clearrepeats
clone
colconcat
colcount
collect
collectasvector
collectwhile
collectwhileasvector
column
columnconcat
columns
compare
concatall
converge
copy
core
count
crosstab
cube
cumcolumn
cumcolumns
cumcolumnswith
cumcolumnwith
cumrow
cumrows
cumrowswith
cumrowwith
cumulate
data
dc
deal
deepcopy
deletecolumn
deleterow
det
determinant
dim
div
divide
dr
drop
dropwhile
dropwhileasvector
eighteenth
eighth
eleventh
equal
equalvalues
eval
except
exec
explode
extract
few
fifteenth
fifth
fillwith
filtermatches
filteroncolumn
filteroncondition
filteronrow
findcellref
first
firstelement
firsthalf
fixat
fjoin
flatten
flip
flipparts
fold
foldl
foldr
forward
fourteenth
fourth
fourths
funcjoin
gettype
graph
graphin
half
halves
hderef
head
headings
hindex
hundredth
i
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ids
implode
inc
include
indices
injoin
insert
insertcolumn
insertrow
inverse
ir
is
is1d
is2d
isFalse
isTrue
islikelytype
isnotnull
isnull
istype
j
joincolumnswith
joinrowswith
joinwith
jq
keep
last
lastelement
list
lookup
make
make1to2d
makecore
makekeyarray
maplist
mapper
maprow
mask
match
matchcolumn
matchindex
matchrow
matchvalue
merge
mergecolumns
mergeio
mergerows
mid
millionth
multiply
nicejoin
nineteenth
nineth
nodeindex
notinclude
notwithinlimits
nth
ntimes
nullifyobjects
numbers
o
objects
of
otherthan
pack
pad
pair
pairmatch
partitiononcondition
parts
pastefolds
pick
pieces
pip
pipall
pipallwithslice
plot
prefix
primitives
print
printf
r
rand
random
remove
removeByVal
removeindices
removewith
repeatntimes
replace
replicate
rest
result
reverselevel
reversepip
reversesort
ri
rotate
rotatecolumns
rotaterows
row
rowconcat
rowcount
rowlengths
rowpush
rows
rslice
second
secondhalf
seq
set
setHeadings
setaxis
setcolumn
setrow
setunit
seventeenth
seventh
shiftlevel
shuffle
sixteenth
sixth
size
size2d
slices
slides
sortrecursively
sortwith
specialprint
spliteach
splitwhile
splitwhileasvector
stringlist
subtract
suchthat
suchthatasvector
suffix
t
table
tablelookup
tail
takewhile
takewhileasvector
tenth
third
thirds
thirteenth
thousandth
tofunctions
toobjectformat
totree
transpose
truefalse
twelfth
twentieth
twod
type
uncrosstab
unimplode
unimplodeleaf
unitsof
unwrapleaf
unzip
value
where
withinlimits
withouttail
x$
xy
xypanel
z3
zero
zip
zoompip

Trial New

5 6 7 5 6 7	0	0	0
0	5 6 7 5 6 7	0	0
1	0	5 6 7 5 6 7	0
0	0	0	5 6 7 5 6 7

Trail 6

${\begin{bmatrix}\alpha _{1}&{\alpha _{1}}^{q}&\cdots &{{\alpha _{1}}^{q}}^{n-1}\\\alpha _{2}&{\alpha _{2}}^{q}&\cdots &{{\alpha _{2}}^{q}}^{n-1}\\\alpha _{3}&{\alpha _{3}}^{q}&\cdots &{{\alpha _{3}}^{q}}^{n-1}\\\vdots &\vdots &\ddots &\vdots \\\alpha _{m}&{\alpha _{m}}^{q}&\cdots &{{\alpha _{m}}^{q}}^{n-1}\\\end{bmatrix}}$

• 2. MATRIX("permutation",18).$\$$_(SUM) = 18
• 3. MATRIX("permutation",5).$\$\$\$$(SUM)=
• 4. MATRIX("permutation",5).$\$\$$(SUM) =

Trail 7

A table in a table

Smoothed Cursive Free Line

Smoothed Cursive Free Line

Smoothed Cursive Free Line