Does anyone have taylor series approximations for tetration and slog base e^(1/e)?

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Does anyone have taylor series approximations for tetration and slog base e^(1/e)?

sheldonison Offline

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05/23/2011, 08:42 PM

(05/23/2011, 07:04 PM)bo198214 Wrote: ....The corresponding super-function developed at 2.03 has then the coefficients:

Code:
0, 1.66, -1.14, 0.839, -0.656, 0.534, -0.448, 0.385, -0.337, 0.300, -0.270, 0.245, -0.225, 0.207, -0.192, 0.179, -0.168, 0.158, -0.149, 0.141

I got my code working for the lower superfunction at \( \eta \), or the sexp. Your results matches the Taylor series I get for \( \text{sexp}_{\eta}(z-1) \), developed at -1, where sexp(-1)=0.

Code:
a0  =  0

a1  =  1.661129667441415

a2  = -1.137387400487982

a3  =  0.841151615164940

a4  = -0.657512962174043

a5  =  0.535494578310460

a6  = -0.449853109363909

a7  =  0.387026076215351

a8  = -0.339240627153272

a9  =  0.301798047541097

a10 = -0.271726518049431

a11 =  0.247071598485337

a12 = -0.226503399721030

a13 =  0.209089537153272

a14 = -0.194158863580830

a15 =  0.181216899324044

a16 = -0.169891743680233

a17 =  0.159898527811493

a18 = -0.151015469479131

a19 =  0.143067376977840

- Sheldon

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Messages In This Thread

Does anyone have taylor series approximations for tetration and slog base e^(1/e)? - by JmsNxn - 05/19/2011, 07:49 PM

RE: Does anyone have taylor series approximations for tetration and slog base e^(1/e)? - by Gottfried - 05/20/2011, 07:34 AM

RE: Does anyone have taylor series approximations for tetration and slog base e^(1/e)? - by JmsNxn - 05/20/2011, 06:34 PM

RE: Does anyone have taylor series approximations for tetration and slog base e^(1/e)? - by andydude - 05/20/2011, 06:43 PM

RE: Does anyone have taylor series approximations for tetration and slog base e^(1/e)? - by JmsNxn - 05/26/2011, 03:18 AM

RE: Does anyone have taylor series approximations for tetration and slog base e^(1/e)? - by Gottfried - 05/21/2011, 02:14 PM

RE: Does anyone have taylor series approximations for tetration and slog base e^(1/e)? - by sheldonison - 05/21/2011, 10:55 PM

RE: Does anyone have taylor series approximations for tetration and slog base e^(1/e)? - by JmsNxn - 06/02/2011, 09:37 PM

RE: Does anyone have taylor series approximations for tetration and slog base e^(1/e)? - by sheldonison - 06/02/2011, 10:27 PM

RE: Does anyone have taylor series approximations for tetration and slog base e^(1/e)? - by JmsNxn - 06/02/2011, 11:40 PM

RE: Does anyone have taylor series approximations for tetration and slog base e^(1/e)? - by sheldonison - 06/03/2011, 12:48 AM

RE: Does anyone have taylor series approximations for tetration and slog base e^(1/e)? - by JmsNxn - 06/05/2011, 06:24 PM

RE: Does anyone have taylor series approximations for tetration and slog base e^(1/e)? - by sheldonison - 06/05/2011, 08:47 PM

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