To illustrate my point a little better, I put together the following comparison of the power series of sexp(z-1) and the power series of ln(z+1):

Edit: always got confused on how to write a shifted series. If it's the sexp centered at -1, it's not sexp(z-(-1)) or sexp(z+1), it's just sexp(z-1). Arrgh! Likewise, ln centered at 1 is ln(z+1).

Code:

`| n | sexp(z-1) | ln(z+1) | difference`

|----+----------------------+----------------------+----------------------

| 0 | 0.000000000000000 | 0.000000000000000 | 0.000000000000000

| 1 | 1.091767351258320 | 1.000000000000000 | 0.091767351258321

| 2 | -0.324494761735111 | -0.500000000000000 | 0.175505238264889

| 3 | 0.349836269767157 | 0.333333333333333 | 0.016502936433824

| 4 | -0.230854426837443 | -0.250000000000000 | 0.019145573162557

| 5 | 0.201330212284523 | 0.200000000000000 | 0.001330212284523

| 6 | -0.164352165253219 | -0.166666666666667 | 0.002314501413448

| 7 | 0.142836335724572 | 0.142857142857143 | -0.000020807132570

| 8 | -0.124694993215245 | -0.125000000000000 | 0.000305006784755

| 9 | 0.111073542269792 | 0.111111111111111 | -0.000037568841319

| 10 | -0.099954567162944 | -0.100000000000000 | 0.000045432837056

| 11 | 0.090897908329423 | 0.090909090909091 | -0.000011182579668

| 12 | -0.083325611455161 | -0.083333333333333 | 0.000007721878172

| 13 | 0.076920407600429 | 0.076923076923077 | -0.000002669322648

| 14 | -0.071427110437354 | -0.071428571428571 | 0.000001460991218

| 15 | 0.066666069650214 | 0.066666666666667 | -0.000000597016452

| 16 | -0.062499703108237 | -0.062500000000000 | 0.000000296891763

| 17 | 0.058823398084957 | 0.058823529411765 | -0.000000131326808

| 18 | -0.055555492550941 | -0.055555555555556 | 0.000000063004615

| 19 | 0.052631550022682 | 0.052631578947368 | -0.000000028924687

| 20 | -0.049999986272057 | -0.050000000000000 | 0.000000013727943

| 21 | 0.047619041200907 | 0.047619047619048 | -0.000000006418141

| 22 | -0.045454542411656 | -0.045454545454546 | 0.000000003042890

| 23 | 0.043478259432923 | 0.043478260869565 | -0.000000001436642

| 24 | -0.041666665984126 | -0.041666666666667 | 0.000000000682540

| 25 | 0.039999999675934 | 0.040000000000000 | -0.000000000324066

Edit: always got confused on how to write a shifted series. If it's the sexp centered at -1, it's not sexp(z-(-1)) or sexp(z+1), it's just sexp(z-1). Arrgh! Likewise, ln centered at 1 is ln(z+1).

~ Jay Daniel Fox