How to write Pearcey functions?

Answer 1

[Ameer Hamza]

You can use integral() function

Pe = @(x, y) integral(@(s) exp(1i*(s.^4 + s.*x + s.^2.*y)), -inf, inf); % first equation
Pe = @(x) integral(@(s) exp(1i*(s.^4 + s.^2.*x)), -inf, inf); % second equation

Answer 2

[Star Strider]

I would code them as:

Pe1 = @(x) integral(@(s) exp(1i*(s.^4 + s.^2.*x)), -Inf, Inf, 'ArrayValued',1);
Pe2 = @(x,y) integral(@(s) exp(1i*(s.^4 + s.*x + s.^2.*y)), -Inf, Inf, 'ArrayValued',1);

These run without error (however not without Warnings, since I am not certain what the arguments should be, and those I tested it with threw Warnings).