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The Riemann zeta function ζ(z) plotted with domain coloring. [1] The pole at = and two zeros on the critical line.. The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (), is a mathematical function of a complex variable defined as () = = = + + + for >, and its analytic continuation elsewhere.
The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.
Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible. It is a general-purpose programming language intended to let programmers write once, run anywhere (), [16] meaning that compiled Java code can run on all platforms that support Java without the need to recompile. [17]
The syntax of Java is the set of rules defining how a Java program is written and interpreted. The syntax is mostly derived from C and C++. Unlike C++, Java has no global functions or variables, but has data members which are also regarded as global variables. All code belongs to classes and all values are objects.
This is a list of the instructions that make up the Java bytecode, an abstract machine language that is ultimately executed by the Java virtual machine. [1] The Java bytecode is generated from languages running on the Java Platform, most notably the Java programming language.
Defines a boolean variable for the values "true" or "false" only. By default, the value of boolean primitive type is false. This keyword is also used to declare that a method returns a value of the primitive type boolean. break Used to end the execution in the current loop body. Used to break out of a switch block. byte
The Stack offers methods to put a new object on the Stack (method push(E e)) and to get objects from the Stack (method pop()). A Stack returns the object according to last-in-first-out (LIFO), e.g. the object which was placed latest on the Stack is returned first. java.util.Stack is a standard implementation of a stack provided by Java.
For nonpositive integer values of s, the zeta function ζ(s − k) in the expansion about μ = 0 reduces to Bernoulli numbers: ζ(−n − k) = −B 1+n+k / (1 + n + k). Numerical evaluation of Li − n ( z ) by this series does not suffer from the cancellation effects that the finite rational expressions given under particular values above ...