Recursive calculus occurrencessuggest textbook on calculusPost-Uni Calculus/Probabilities Book SuggestionPrerequisites of general calculusReference help - Linear Algebra and CalculusA closed form of $sum_k=0^inftyfrac(-1)^k+1k!Gamma^2left(frack2right)$What calculus material can prepare me for MCMC?Book recommendation for differential and integral calculus of one and of several variablesCalculus book that starts with sequencesSoft question: What are some good calculus resourcesGood books on Calculus and Geometry
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Recursive calculus occurrences
suggest textbook on calculusPost-Uni Calculus/Probabilities Book SuggestionPrerequisites of general calculusReference help - Linear Algebra and CalculusA closed form of $sum_k=0^inftyfrac(-1)^k+1k!Gamma^2left(frack2right)$What calculus material can prepare me for MCMC?Book recommendation for differential and integral calculus of one and of several variablesCalculus book that starts with sequencesSoft question: What are some good calculus resourcesGood books on Calculus and Geometry
$begingroup$
I am looking for recursive definitionss in high school calculus. These could be series with a general terms and other interesting observations.
Please share any recursive definitions in calculus you are aware of.
calculus
asked Mar 14 at 15:45
01110000_0111000001110000_01110000
267
$endgroup$
add a comment |
$begingroup$
I am looking for recursive definitionss in high school calculus. These could be series with a general terms and other interesting observations.
Please share any recursive definitions in calculus you are aware of.
calculus
asked Mar 14 at 15:45
01110000_0111000001110000_01110000
267
$endgroup$
$begingroup$
do you mean recursive definitions? almost anything defined as a sequence can have a recursive definition...
$endgroup$
– gt6989b
Mar 14 at 15:50
$begingroup$
Yes, I meant recursive definitions.
$endgroup$
– 01110000_01110000
Mar 14 at 15:51
add a comment |
$begingroup$
I am looking for recursive definitionss in high school calculus. These could be series with a general terms and other interesting observations.
Please share any recursive definitions in calculus you are aware of.
calculus
asked Mar 14 at 15:45
01110000_0111000001110000_01110000
267
$endgroup$
I am looking for recursive definitionss in high school calculus. These could be series with a general terms and other interesting observations.
Please share any recursive definitions in calculus you are aware of.
calculus
calculus
asked Mar 14 at 15:45
01110000_0111000001110000_01110000
267
asked Mar 14 at 15:45
01110000_0111000001110000_01110000
267
edited Mar 14 at 15:51
01110000_01110000
asked Mar 14 at 15:45
01110000_0111000001110000_01110000
267
asked Mar 14 at 15:45
01110000_0111000001110000_01110000
267
asked Mar 14 at 15:45
01110000_0111000001110000_01110000
267
267
$begingroup$
do you mean recursive definitions? almost anything defined as a sequence can have a recursive definition...
$endgroup$
– gt6989b
Mar 14 at 15:50
$begingroup$
Yes, I meant recursive definitions.
$endgroup$
– 01110000_01110000
Mar 14 at 15:51
add a comment |
$begingroup$
do you mean recursive definitions? almost anything defined as a sequence can have a recursive definition...
$endgroup$
– gt6989b
Mar 14 at 15:50
$begingroup$
Yes, I meant recursive definitions.
$endgroup$
– 01110000_01110000
Mar 14 at 15:51
$begingroup$
do you mean recursive definitions? almost anything defined as a sequence can have a recursive definition...
$endgroup$
– gt6989b
Mar 14 at 15:50
$begingroup$
do you mean recursive definitions? almost anything defined as a sequence can have a recursive definition...
$endgroup$
– gt6989b
Mar 14 at 15:50
$begingroup$
Yes, I meant recursive definitions.
$endgroup$
– 01110000_01110000
Mar 14 at 15:51
$begingroup$
Yes, I meant recursive definitions.
$endgroup$
– 01110000_01110000
Mar 14 at 15:51
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Not sure what you are asking for exactly and why do you need it, but here are some famous examples.
Factorial The factorial, related to the $Gamma$ function, is defined as
$$n! = 1 times 2 times ldots times n = prod_k=1^n k$$
but can alternatively be defined as $0! = 1$ and $n! = n cdot (n-1)!$Fibonacci Sequence The sequence
$$
beginsplit
F_n &= fracphi^n -psi^nphi - psi = fracphi^n -psi^nsqrt5 \
phi &= frac1 + sqrt52 \
psi &= frac1 - sqrt52
endsplit
$$
can be defined recursively as $F_n+2 = F_n+1 + F_n, F_0 = 0, F_1 = 1$.The number $$e = lim_n to infty left(1 + frac1nright)^n$$ can be instead defined as the limit of the sequence $$e_1 = 2, e_n+1 = left(e_n^1/n - frac1n(n+1)right)^n+1.$$
answered Mar 14 at 18:02
gt6989bgt6989b
35k22557
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Not sure what you are asking for exactly and why do you need it, but here are some famous examples.
Factorial The factorial, related to the $Gamma$ function, is defined as
$$n! = 1 times 2 times ldots times n = prod_k=1^n k$$
but can alternatively be defined as $0! = 1$ and $n! = n cdot (n-1)!$Fibonacci Sequence The sequence
$$
beginsplit
F_n &= fracphi^n -psi^nphi - psi = fracphi^n -psi^nsqrt5 \
phi &= frac1 + sqrt52 \
psi &= frac1 - sqrt52
endsplit
$$
can be defined recursively as $F_n+2 = F_n+1 + F_n, F_0 = 0, F_1 = 1$.The number $$e = lim_n to infty left(1 + frac1nright)^n$$ can be instead defined as the limit of the sequence $$e_1 = 2, e_n+1 = left(e_n^1/n - frac1n(n+1)right)^n+1.$$
answered Mar 14 at 18:02
gt6989bgt6989b
35k22557
$endgroup$
add a comment |
$begingroup$
Not sure what you are asking for exactly and why do you need it, but here are some famous examples.
Factorial The factorial, related to the $Gamma$ function, is defined as
$$n! = 1 times 2 times ldots times n = prod_k=1^n k$$
but can alternatively be defined as $0! = 1$ and $n! = n cdot (n-1)!$Fibonacci Sequence The sequence
$$
beginsplit
F_n &= fracphi^n -psi^nphi - psi = fracphi^n -psi^nsqrt5 \
phi &= frac1 + sqrt52 \
psi &= frac1 - sqrt52
endsplit
$$
can be defined recursively as $F_n+2 = F_n+1 + F_n, F_0 = 0, F_1 = 1$.The number $$e = lim_n to infty left(1 + frac1nright)^n$$ can be instead defined as the limit of the sequence $$e_1 = 2, e_n+1 = left(e_n^1/n - frac1n(n+1)right)^n+1.$$
answered Mar 14 at 18:02
gt6989bgt6989b
35k22557
$endgroup$
add a comment |
$begingroup$
Not sure what you are asking for exactly and why do you need it, but here are some famous examples.
Factorial The factorial, related to the $Gamma$ function, is defined as
$$n! = 1 times 2 times ldots times n = prod_k=1^n k$$
but can alternatively be defined as $0! = 1$ and $n! = n cdot (n-1)!$Fibonacci Sequence The sequence
$$
beginsplit
F_n &= fracphi^n -psi^nphi - psi = fracphi^n -psi^nsqrt5 \
phi &= frac1 + sqrt52 \
psi &= frac1 - sqrt52
endsplit
$$
can be defined recursively as $F_n+2 = F_n+1 + F_n, F_0 = 0, F_1 = 1$.The number $$e = lim_n to infty left(1 + frac1nright)^n$$ can be instead defined as the limit of the sequence $$e_1 = 2, e_n+1 = left(e_n^1/n - frac1n(n+1)right)^n+1.$$
answered Mar 14 at 18:02
gt6989bgt6989b
35k22557
$endgroup$
Not sure what you are asking for exactly and why do you need it, but here are some famous examples.
Factorial The factorial, related to the $Gamma$ function, is defined as
$$n! = 1 times 2 times ldots times n = prod_k=1^n k$$
but can alternatively be defined as $0! = 1$ and $n! = n cdot (n-1)!$Fibonacci Sequence The sequence
$$
beginsplit
F_n &= fracphi^n -psi^nphi - psi = fracphi^n -psi^nsqrt5 \
phi &= frac1 + sqrt52 \
psi &= frac1 - sqrt52
endsplit
$$
can be defined recursively as $F_n+2 = F_n+1 + F_n, F_0 = 0, F_1 = 1$.The number $$e = lim_n to infty left(1 + frac1nright)^n$$ can be instead defined as the limit of the sequence $$e_1 = 2, e_n+1 = left(e_n^1/n - frac1n(n+1)right)^n+1.$$
answered Mar 14 at 18:02
gt6989bgt6989b
35k22557
answered Mar 14 at 18:02
gt6989bgt6989b
35k22557
answered Mar 14 at 18:02
gt6989bgt6989b
35k22557
answered Mar 14 at 18:02
gt6989bgt6989b
35k22557
35k22557
add a comment |
add a comment |
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$begingroup$
do you mean recursive definitions? almost anything defined as a sequence can have a recursive definition...
$endgroup$
– gt6989b
Mar 14 at 15:50
$begingroup$
Yes, I meant recursive definitions.
$endgroup$
– 01110000_01110000
Mar 14 at 15:51