Wolfram Cloud Document

p[x_,t_]:=1-Erf[x/Sqrt[4*t]]

pa[x_,t_]:=1

1/4

t

NIntegrate

HypergeometricPFQ{},

1

2

,

3

4

,-

4

s

256t



Gamma

3

4



-

sHypergeometricPFQ{},

3

4

,

5

4

,-

4

s

256t



π

1/4

t

+

2

s

HypergeometricPFQ{},

5

4

,

3

2

,-

4

s

256t



2

t

Gamma

1

4



-

1

4

s

500*Pi*(4^4)t



*p[x,s],{s,0,Infinity},MinRecursion4,AccuracyGoal60,PrecisionGoal4,WorkingPrecision150

Plot[{Log[10,1-pa[0.1,10^t]]},{t,-3,8},PlotRangeAll,AxesLabel{Log[t],Log[1-P_0.5[x,t]]}]