Thread: Can this series be represented by a function

Hello,

The infinite series

might also be expressed

where is the jth integral of x, and

Again, this series can be expressed in the function

Now, my question is does there exist a function that expresses the series

where is the jth *derivative* of x?

(...and I guess or something like that)


Thanks

Originally Posted by rainer

Hello,

The infinite series

might also be expressed

where is the jth integral of x, and

No, it isn't. The "jth integral of x" is , not .
The exponential function, , has the property you are talking about.

Again, this series can be expressed in the function

Now, my question is does there exist a function that expresses the series

where is the jth *derivative* of x?

??? the first derivative of x is 1 and the "jth derivative of x" for j> 1 is 0. So such a series would be x+ 1+ 0+ 0+ 0...= x+ 1.

(...and I guess or something like that)


Thanks