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Is there General Formula for an nth Order Central Finite Difference
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I am searching for a general formula for directly calculating the second, fourth, and sixth derivative directly from a time series data. Wikipedia has a formula for finding an $n$th order central finite difference. I have searched a lot of places but I cannot find it in any reference book? The equation is given on a Wikipedia page under the section "Higher Order Difference."
https://en.wikipedia.org/wiki/Finite_difference
Does anyone know a good reference where one can find a general formula for nth order finite difference?
calculus differential-equations derivatives reference-request numerical-methods
edited Jul 20 at 15:33
user7530
33.4k558109
asked Jul 20 at 14:55
M. Farooq
83
add a comment |Â
up vote
0
down vote
favorite
I am searching for a general formula for directly calculating the second, fourth, and sixth derivative directly from a time series data. Wikipedia has a formula for finding an $n$th order central finite difference. I have searched a lot of places but I cannot find it in any reference book? The equation is given on a Wikipedia page under the section "Higher Order Difference."
https://en.wikipedia.org/wiki/Finite_difference
Does anyone know a good reference where one can find a general formula for nth order finite difference?
calculus differential-equations derivatives reference-request numerical-methods
edited Jul 20 at 15:33
user7530
33.4k558109
asked Jul 20 at 14:55
M. Farooq
83
You can find "The Calculus of Observations" by Whittaker and Robinson scanned oopy. Chapter III is Central DIfference Formulae and the next Chapter IV is Applications of Difference Formulae. Page 64 and 65 is derivatives in terms of central differences.
– Somos
Jul 20 at 16:11
Thank you for the link. I will check.
– M. Farooq
Jul 20 at 16:48
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am searching for a general formula for directly calculating the second, fourth, and sixth derivative directly from a time series data. Wikipedia has a formula for finding an $n$th order central finite difference. I have searched a lot of places but I cannot find it in any reference book? The equation is given on a Wikipedia page under the section "Higher Order Difference."
https://en.wikipedia.org/wiki/Finite_difference
Does anyone know a good reference where one can find a general formula for nth order finite difference?
calculus differential-equations derivatives reference-request numerical-methods
edited Jul 20 at 15:33
user7530
33.4k558109
asked Jul 20 at 14:55
M. Farooq
83
I am searching for a general formula for directly calculating the second, fourth, and sixth derivative directly from a time series data. Wikipedia has a formula for finding an $n$th order central finite difference. I have searched a lot of places but I cannot find it in any reference book? The equation is given on a Wikipedia page under the section "Higher Order Difference."
https://en.wikipedia.org/wiki/Finite_difference
Does anyone know a good reference where one can find a general formula for nth order finite difference?
calculus differential-equations derivatives reference-request numerical-methods
edited Jul 20 at 15:33
user7530
33.4k558109
asked Jul 20 at 14:55
M. Farooq
83
edited Jul 20 at 15:33
user7530
33.4k558109
edited Jul 20 at 15:33
user7530
33.4k558109
edited Jul 20 at 15:33
user7530
33.4k558109
33.4k558109
asked Jul 20 at 14:55
M. Farooq
83
asked Jul 20 at 14:55
M. Farooq
83
asked Jul 20 at 14:55
M. Farooq
83
83
You can find "The Calculus of Observations" by Whittaker and Robinson scanned oopy. Chapter III is Central DIfference Formulae and the next Chapter IV is Applications of Difference Formulae. Page 64 and 65 is derivatives in terms of central differences.
– Somos
Jul 20 at 16:11
Thank you for the link. I will check.
– M. Farooq
Jul 20 at 16:48
add a comment |Â
You can find "The Calculus of Observations" by Whittaker and Robinson scanned oopy. Chapter III is Central DIfference Formulae and the next Chapter IV is Applications of Difference Formulae. Page 64 and 65 is derivatives in terms of central differences.
– Somos
Jul 20 at 16:11
Thank you for the link. I will check.
– M. Farooq
Jul 20 at 16:48
You can find "The Calculus of Observations" by Whittaker and Robinson scanned oopy. Chapter III is Central DIfference Formulae and the next Chapter IV is Applications of Difference Formulae. Page 64 and 65 is derivatives in terms of central differences.
– Somos
Jul 20 at 16:11
You can find "The Calculus of Observations" by Whittaker and Robinson scanned oopy. Chapter III is Central DIfference Formulae and the next Chapter IV is Applications of Difference Formulae. Page 64 and 65 is derivatives in terms of central differences.
– Somos
Jul 20 at 16:11
Thank you for the link. I will check.
– M. Farooq
Jul 20 at 16:48
Thank you for the link. I will check.
– M. Farooq
Jul 20 at 16:48
add a comment |Â
1 Answer
1
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0
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Wikipedia articles come with extensive lists of references. Just picking one promising-looking reference at random (Calculus of Finite Differences by Jordan) I found a section on central differences including the general formulas for $n$th order central differences (they're written in terms of other formulas for forward differences, but putting the pieces together is straightfoward).
answered Jul 20 at 15:43
user7530
33.4k558109
Thank you, I checked the first few reference books listed there, but none of them give the exactly show the same relationship as listed there. Also got hold of Jordan's book (1950). The notation is very different. It does not have the same formulae as given in Wikipedia under Higher Order Difference. I am searching this out of curiosity if any other book shows the same equations (written in similar modern notation as in Wikipedia). That section does not have any citation.
– M. Farooq
Jul 20 at 16:09
@M.Farooq I don't understand why you need the exact same notation. Surely you can change the notation yourself to suit your needs? Or just use the formula in Wikipedia?
– user7530
Jul 20 at 16:20
Thanks, I just wanted to confirm if the nth order central difference formula in Wikipedia is correct. I am a chemist, trying to implement this in Excel to see higher order even derivatives of a chromatographic peak directly without all derivatives in series (1st, then, 2nd, 3rd and so on). This was the reason for searching a general relation to directly check 2nd, 4th, 6th etc.
– M. Farooq
Jul 20 at 16:47
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Wikipedia articles come with extensive lists of references. Just picking one promising-looking reference at random (Calculus of Finite Differences by Jordan) I found a section on central differences including the general formulas for $n$th order central differences (they're written in terms of other formulas for forward differences, but putting the pieces together is straightfoward).
answered Jul 20 at 15:43
user7530
33.4k558109
Thank you, I checked the first few reference books listed there, but none of them give the exactly show the same relationship as listed there. Also got hold of Jordan's book (1950). The notation is very different. It does not have the same formulae as given in Wikipedia under Higher Order Difference. I am searching this out of curiosity if any other book shows the same equations (written in similar modern notation as in Wikipedia). That section does not have any citation.
– M. Farooq
Jul 20 at 16:09
@M.Farooq I don't understand why you need the exact same notation. Surely you can change the notation yourself to suit your needs? Or just use the formula in Wikipedia?
– user7530
Jul 20 at 16:20
Thanks, I just wanted to confirm if the nth order central difference formula in Wikipedia is correct. I am a chemist, trying to implement this in Excel to see higher order even derivatives of a chromatographic peak directly without all derivatives in series (1st, then, 2nd, 3rd and so on). This was the reason for searching a general relation to directly check 2nd, 4th, 6th etc.
– M. Farooq
Jul 20 at 16:47
add a comment |Â
up vote
0
down vote
Wikipedia articles come with extensive lists of references. Just picking one promising-looking reference at random (Calculus of Finite Differences by Jordan) I found a section on central differences including the general formulas for $n$th order central differences (they're written in terms of other formulas for forward differences, but putting the pieces together is straightfoward).
answered Jul 20 at 15:43
user7530
33.4k558109
Thank you, I checked the first few reference books listed there, but none of them give the exactly show the same relationship as listed there. Also got hold of Jordan's book (1950). The notation is very different. It does not have the same formulae as given in Wikipedia under Higher Order Difference. I am searching this out of curiosity if any other book shows the same equations (written in similar modern notation as in Wikipedia). That section does not have any citation.
– M. Farooq
Jul 20 at 16:09
@M.Farooq I don't understand why you need the exact same notation. Surely you can change the notation yourself to suit your needs? Or just use the formula in Wikipedia?
– user7530
Jul 20 at 16:20
Thanks, I just wanted to confirm if the nth order central difference formula in Wikipedia is correct. I am a chemist, trying to implement this in Excel to see higher order even derivatives of a chromatographic peak directly without all derivatives in series (1st, then, 2nd, 3rd and so on). This was the reason for searching a general relation to directly check 2nd, 4th, 6th etc.
– M. Farooq
Jul 20 at 16:47
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Wikipedia articles come with extensive lists of references. Just picking one promising-looking reference at random (Calculus of Finite Differences by Jordan) I found a section on central differences including the general formulas for $n$th order central differences (they're written in terms of other formulas for forward differences, but putting the pieces together is straightfoward).
answered Jul 20 at 15:43
user7530
33.4k558109
Wikipedia articles come with extensive lists of references. Just picking one promising-looking reference at random (Calculus of Finite Differences by Jordan) I found a section on central differences including the general formulas for $n$th order central differences (they're written in terms of other formulas for forward differences, but putting the pieces together is straightfoward).
answered Jul 20 at 15:43
user7530
33.4k558109
answered Jul 20 at 15:43
user7530
33.4k558109
answered Jul 20 at 15:43
user7530
33.4k558109
answered Jul 20 at 15:43
user7530
33.4k558109
33.4k558109
Thank you, I checked the first few reference books listed there, but none of them give the exactly show the same relationship as listed there. Also got hold of Jordan's book (1950). The notation is very different. It does not have the same formulae as given in Wikipedia under Higher Order Difference. I am searching this out of curiosity if any other book shows the same equations (written in similar modern notation as in Wikipedia). That section does not have any citation.
– M. Farooq
Jul 20 at 16:09
@M.Farooq I don't understand why you need the exact same notation. Surely you can change the notation yourself to suit your needs? Or just use the formula in Wikipedia?
– user7530
Jul 20 at 16:20
Thanks, I just wanted to confirm if the nth order central difference formula in Wikipedia is correct. I am a chemist, trying to implement this in Excel to see higher order even derivatives of a chromatographic peak directly without all derivatives in series (1st, then, 2nd, 3rd and so on). This was the reason for searching a general relation to directly check 2nd, 4th, 6th etc.
– M. Farooq
Jul 20 at 16:47
add a comment |Â
Thank you, I checked the first few reference books listed there, but none of them give the exactly show the same relationship as listed there. Also got hold of Jordan's book (1950). The notation is very different. It does not have the same formulae as given in Wikipedia under Higher Order Difference. I am searching this out of curiosity if any other book shows the same equations (written in similar modern notation as in Wikipedia). That section does not have any citation.
– M. Farooq
Jul 20 at 16:09
@M.Farooq I don't understand why you need the exact same notation. Surely you can change the notation yourself to suit your needs? Or just use the formula in Wikipedia?
– user7530
Jul 20 at 16:20
Thanks, I just wanted to confirm if the nth order central difference formula in Wikipedia is correct. I am a chemist, trying to implement this in Excel to see higher order even derivatives of a chromatographic peak directly without all derivatives in series (1st, then, 2nd, 3rd and so on). This was the reason for searching a general relation to directly check 2nd, 4th, 6th etc.
– M. Farooq
Jul 20 at 16:47
Thank you, I checked the first few reference books listed there, but none of them give the exactly show the same relationship as listed there. Also got hold of Jordan's book (1950). The notation is very different. It does not have the same formulae as given in Wikipedia under Higher Order Difference. I am searching this out of curiosity if any other book shows the same equations (written in similar modern notation as in Wikipedia). That section does not have any citation.
– M. Farooq
Jul 20 at 16:09
Thank you, I checked the first few reference books listed there, but none of them give the exactly show the same relationship as listed there. Also got hold of Jordan's book (1950). The notation is very different. It does not have the same formulae as given in Wikipedia under Higher Order Difference. I am searching this out of curiosity if any other book shows the same equations (written in similar modern notation as in Wikipedia). That section does not have any citation.
– M. Farooq
Jul 20 at 16:09
@M.Farooq I don't understand why you need the exact same notation. Surely you can change the notation yourself to suit your needs? Or just use the formula in Wikipedia?
– user7530
Jul 20 at 16:20
@M.Farooq I don't understand why you need the exact same notation. Surely you can change the notation yourself to suit your needs? Or just use the formula in Wikipedia?
– user7530
Jul 20 at 16:20
Thanks, I just wanted to confirm if the nth order central difference formula in Wikipedia is correct. I am a chemist, trying to implement this in Excel to see higher order even derivatives of a chromatographic peak directly without all derivatives in series (1st, then, 2nd, 3rd and so on). This was the reason for searching a general relation to directly check 2nd, 4th, 6th etc.
– M. Farooq
Jul 20 at 16:47
Thanks, I just wanted to confirm if the nth order central difference formula in Wikipedia is correct. I am a chemist, trying to implement this in Excel to see higher order even derivatives of a chromatographic peak directly without all derivatives in series (1st, then, 2nd, 3rd and so on). This was the reason for searching a general relation to directly check 2nd, 4th, 6th etc.
– M. Farooq
Jul 20 at 16:47
add a comment |Â
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You can find "The Calculus of Observations" by Whittaker and Robinson scanned oopy. Chapter III is Central DIfference Formulae and the next Chapter IV is Applications of Difference Formulae. Page 64 and 65 is derivatives in terms of central differences.
– Somos
Jul 20 at 16:11
Thank you for the link. I will check.
– M. Farooq
Jul 20 at 16:48