How to make a Java Generic method static?

You need to move type parameter to the method level to indicate that you have a generic method rather than generic class:

public class ArrayUtils {
    public static <T> E[] appendToArray(E[] array, E item) {
        E[] result = (E[])new Object[array.length+1];
        result[array.length] = item;
        return result;
    }
}

the only thing you can do is to change your signature to

public static <E> E[] appendToArray(E[] array, E item)

Important details:

Generic expressions preceding the return value always introduce (declare) a new generic type variable.

Additionally, type variables between types (ArrayUtils) and static methods (appendToArray) never interfere with each other.

So, what does this mean: In my answer <E> would hide the E from ArrayUtils<E> if the method wouldn't be static. AND <E> has nothing to do with the E from ArrayUtils<E>.

To reflect this fact better, a more correct answer would be:

public static <I> I[] appendToArray(I[] array, I item)

public static <E> E[] appendToArray(E[] array, E item) { ...

Note the <E>.

Static generic methods need their own generic declaration (public static <E>) separate from the class's generic declaration (public class ArrayUtils<E>).

If the compiler complains about a type ambiguity in invoking a static generic method (again not likely in your case, but, generally speaking, just in case), here's how to explicitly invoke a static generic method using a specific type (_class_.<_generictypeparams_>_methodname_):

String[] newStrings = ArrayUtils.<String>appendToArray(strings, "another string");

This would only happen if the compiler can't determine the generic type because, e.g. the generic type isn't related to the method arguments.

I'll explain it in a simple way.

Generics defined at Class level are completely separate from the generics defined at the (static) method level.

class Greet<T> {

    public static <T> void sayHello(T obj) {
        System.out.println("Hello " + obj);
    }
}

When you see the above code anywhere, please note that the T defined at the class level has nothing to do with the T defined in the static method. The following code is also completely valid and equivalent to the above code.

class Greet<T> {

    public static <E> void sayHello(E obj) {
        System.out.println("Hello " + obj);
    }
}

Why the static method needs to have its own generics separate from those of the Class?

This is because, the static method can be called without even instantiating the Class. So if the Class is not yet instantiated, we do not yet know what is T. This is the reason why the static methods needs to have its own generics.

So, whenever you are calling the static method,

Greet.sayHello("Bob");
Greet.sayHello(123);

JVM interprets it as the following.

Greet.<String>sayHello("Bob");
Greet.<Integer>sayHello(123);

Both giving the same outputs.

Hello Bob
Hello 123