Wolfram Cloud Document

In[]:=

ClearAll["`*"];Remove["`*"];

In[]:=

p[x_,t_]:=1-Erf[x/Sqrt[4*t]];pa[x_?NumericQ,t_?NumericQ]:=1

1/4

t

NIntegrate

HypergeometricPFQ{},

1

2

,

3

4

,-

4

s

256t



Gamma

3

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-

sHypergeometricPFQ{},

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,

5

4

,-

4

s

256t



π

1/4

t

+

2

s

HypergeometricPFQ{},

5

4

,

3

2

,-

4

s

256t



2

t

Gamma

1

4



*p[x,s],{s,0,Infinity},Method"LocalAdaptive",PrecisionGoal20(*IncreasethePrecisionGoal.Theresultwillbemoreaccurateattheexpenseofcomputationtime.*)

In[]:=

n=3;ListLinePlot[Table[{t,Log[10,1-pa[1/10,10^t]]},{t,-3,2,n^-1}],AxesLabel{Log[t],Log[1-P_0.5[x,t]]}](*Increasethenparameter.Thegraphwillbemoreaccurateattheexpenseofcomputationtime.*)

Out[]=

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