To compute the function signature offchain and use it in interaction with smart contract function probably with calldata you will probably use either ethers.js or web3 library so this is how you get that function hash and first four bytes that are used in function definitions in solidity

ethers.utils.keccak256(ethers.utils.toUtf8Bytes("initialize")).substr(0, 10) or web3.utils.sha3('initialize()').substr(0, 10)

both will result in this output 0x8129fc1c which can later be applied for example in constructor with proxy contract where this function gets called with delegatecall (bytes memory constructData)

    constructor(bytes memory constructData, address contractLogic) {
        // save the code address
        assembly { // solium-disable-line
            sstore(0xc5f16f0fcc639fa48a6947836d9850f504798523bf8c9a3a87d5876cf622bcf7, contractLogic)
        }
        (bool success, bytes memory result ) = contractLogic.delegatecall(constructData); // solium-disable-line
        require(success, "Construction failed");
    }

To compute the function signature offchain and use it in interaction with smart contract function probably with calldata you will probably use either ethers.js or web3 library so this is how you get that function hash and first four bytes that are used in function definitions in solidity

ethers.utils.keccak256(ethers.utils.toUtf8Bytes("initialize")).substr(0, 10) or web3.utils.sha3('initialize()').substr(0, 10)

both will result in this output 0x8129fc1c which can later be applied for example in constructor with proxy contract where this function gets called with delegatecall (bytes memory constructData)

    constructor(bytes memory constructData, address contractLogic) {
        // save the code address
        assembly { // solium-disable-line
            sstore(0xc5f16f0fcc639fa48a6947836d9850f504798523bf8c9a3a87d5876cf622bcf7, contractLogic)
        }
        (bool success, bytes memory result ) = contractLogic.delegatecall(constructData); // solium-disable-line
        require(success, "Construction failed");
    }