In finding almost rational number I have this :
Define : $$f\left(x\right)=e^{x}-1-x-\frac{x^{2}}{2}-\frac{x^{3}}{6}-\frac{x^{4}}{24}$$ $$h\left(x\right)=f\left(x\right)+f\left(a\right)-f\left(x^{\frac{x}{x+a}}a^{\frac{a}{x+a}}-x-a\right)-f\left(\frac{xf'\left(x\right)+af'\left(a\right)}{f'\left(x\right)+f'\left(a\right)}\right)$$
Now consider for $a=2$:
$$h\left(35\right)-h\left(34\right)$$
My computer say that the result of this difference is $7.25$ and I think there is a miscalculations
Can someone tells me where is the mistake ?
If it's not an decimal number is it new ?
This is an interesting problem. Using Mathematica
N[h(35)]$=96.25$ $\qquad \qquad$N[h(34)]$=89.$N[h(35),6]$=97.2574$ $\qquad \qquad$N[h(34),6]$=93.7003$I thought that these two instrauction where the same
N[Pi^Pi^Pi]$=1.34016 \times 10^{18}$N[Pi^Pi^Pi,6]$=1.34016 \times 10^{18}$