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
Multi tool use
Which was the first story featuring espers?
What is the highest possible scrabble score for placing a single tile
Has the laser at Magurele, Romania reached a tenth of the Sun's power?
What fields between the rationals and the reals allow a good notion of 2D distance?
What does "Scientists rise up against statistical significance" mean? (Comment in Nature)
The Digit Triangles
Is there a RAID 0 Equivalent for RAM?
Does Doodling or Improvising on the Piano Have Any Benefits?
Is there a nicer/politer/more positive alternative for "negates"?
Why do ¬, ∀ and ∃ have the same precedence?
How can ping know if my host is down
How to explain what's wrong with this application of the chain rule?
Can I cause damage to electrical appliances by unplugging them when they are turned on?
Did the UK lift the requirement for registering SIM cards?
Multiplicative persistence
Why can't the Brexit deadlock in the UK parliament be solved with a plurality vote?
How could a planet have erratic days?
Giving feedback to someone without sounding prejudiced
Circuit Analysis: Obtaining Close Loop OP - AMP Transfer function
Delete multiple columns using awk or sed
Why does AES have exactly 10 rounds for a 128-bit key, 12 for 192 bits and 14 for a 256-bit key size?
What's the name of the logical fallacy where a debater extends a statement far beyond the original statement to make it true?
Quoting Keynes in a lecture
Which Article Helped Get Rid of Technobabble in RPGs?
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 |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3148163%2frecursive-calculus-occurrences%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
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 |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3148163%2frecursive-calculus-occurrences%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Ooksew9Qc uPj,G,LGfq2PoNjo M,QlOZOLTXaF2m2ZxW0leXlKu0 z,PRtma,HmOz6sTsM MlZs
$begingroup$
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