{"id":24975685,"url":"https://github.com/stdlib-js/math-base-tools-sum-series","last_synced_at":"2025-04-11T12:50:44.674Z","repository":{"id":41363969,"uuid":"377225217","full_name":"stdlib-js/math-base-tools-sum-series","owner":"stdlib-js","description":"Compute the sum of an infinite series.","archived":false,"fork":false,"pushed_at":"2025-04-07T00:48:09.000Z","size":407,"stargazers_count":1,"open_issues_count":0,"forks_count":0,"subscribers_count":3,"default_branch":"main","last_synced_at":"2025-04-07T01:27:31.078Z","etag":null,"topics":["expansion","fraction","javascript","math","mathematics","node","node-js","nodejs","series","stdlib"],"latest_commit_sha":null,"homepage":"https://github.com/stdlib-js/stdlib","language":"JavaScript","has_issues":false,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"apache-2.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/stdlib-js.png","metadata":{"files":{"readme":"README.md","changelog":"CHANGELOG.md","contributing":"CONTRIBUTING.md","funding":null,"license":"LICENSE","code_of_conduct":"CODE_OF_CONDUCT.md","threat_model":null,"audit":null,"citation":"CITATION.cff","codeowners":null,"security":"SECURITY.md","support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null},"funding":{"github":["stdlib-js"],"open_collective":"stdlib","tidelift":"npm/@stdlib/stdlib"}},"created_at":"2021-06-15T16:20:11.000Z","updated_at":"2025-04-07T00:38:46.000Z","dependencies_parsed_at":"2023-09-24T05:46:06.701Z","dependency_job_id":"52c11538-1ece-4a72-b24c-b6ba085ec397","html_url":"https://github.com/stdlib-js/math-base-tools-sum-series","commit_stats":{"total_commits":46,"total_committers":1,"mean_commits":46.0,"dds":0.0,"last_synced_commit":"d5fa3d41525dc3aa28d202ce33b8225e663d64b1"},"previous_names":[],"tags_count":22,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fmath-base-tools-sum-series","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fmath-base-tools-sum-series/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fmath-base-tools-sum-series/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fmath-base-tools-sum-series/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/stdlib-js","download_url":"https://codeload.github.com/stdlib-js/math-base-tools-sum-series/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":248402656,"owners_count":21097338,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["expansion","fraction","javascript","math","mathematics","node","node-js","nodejs","series","stdlib"],"created_at":"2025-02-03T21:45:48.085Z","updated_at":"2025-04-11T12:50:44.659Z","avatar_url":"https://github.com/stdlib-js.png","language":"JavaScript","readme":"\u003c!--\n\n@license Apache-2.0\n\nCopyright (c) 2018 The Stdlib Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n   http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n\n--\u003e\n\n\n\u003cdetails\u003e\n  \u003csummary\u003e\n    About stdlib...\n  \u003c/summary\u003e\n  \u003cp\u003eWe believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.\u003c/p\u003e\n  \u003cp\u003eThe library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.\u003c/p\u003e\n  \u003cp\u003eWhen you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.\u003c/p\u003e\n  \u003cp\u003eTo join us in bringing numerical computing to the web, get started by checking us out on \u003ca href=\"https://github.com/stdlib-js/stdlib\"\u003eGitHub\u003c/a\u003e, and please consider \u003ca href=\"https://opencollective.com/stdlib\"\u003efinancially supporting stdlib\u003c/a\u003e. We greatly appreciate your continued support!\u003c/p\u003e\n\u003c/details\u003e\n\n# sum-series\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] \u003c!-- [![dependencies][dependencies-image]][dependencies-url] --\u003e\n\n\u003e Compute the sum of an [infinite series][infinite-series].\n\n\u003csection class=\"installation\"\u003e\n\n## Installation\n\n```bash\nnpm install @stdlib/math-base-tools-sum-series\n```\n\nAlternatively,\n\n-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).\n-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).\n-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).\n\nThe [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.\n\nTo view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.\n\n\u003c/section\u003e\n\n\u003csection class=\"usage\"\u003e\n\n## Usage\n\n```javascript\nvar sumSeries = require( '@stdlib/math-base-tools-sum-series' );\n```\n\n#### sumSeries( generator\\[, options ] )\n\nComputes the sum of the series given by the supplied `generator` argument. `generator` can be either an ES6 [Generator object][es6-generator] or a function which returns successive elements of the series at each invocation.\n\nUsing an ES6 [Generator object][es6-generator]:\n\n\u003c!-- eslint-disable no-restricted-syntax, node/no-unsupported-features/es-syntax --\u003e\n\n```javascript\nvar pow = require( '@stdlib/math-base-special-pow' );\nvar gen = geometricSeriesGenerator( 0.9 );\nvar out = sumSeries( gen );\n// returns 10\n\nfunction* geometricSeriesGenerator( x ) {\n    var exponent = 0;\n    while ( true ) {\n        yield pow( x, exponent );\n        exponent += 1;\n    }\n}\n```\n\nAlternatively, one can use a closure to achieve the same goal:\n\n```javascript\nvar pow = require( '@stdlib/math-base-special-pow' );\nvar gen = geometricSeriesClosure( 0.9 );\nvar out = sumSeries( gen );\n// returns 10\n\nfunction geometricSeriesClosure( x ) {\n    var exponent = -1;\n    return gen;\n\n    function gen() {\n        exponent += 1;\n        return pow( x, exponent );\n    }\n}\n```\n\nThe `function` accepts the following `options`:\n\n-   **maxTerms**: integer denoting the maximum number of terms to be summed. Default: `1000000`.\n-   **tolerance**: number specifying the tolerance used to assess convergence. Default: `2.22e-16`.\n-   **initialValue**: number specifying the initial value of the returned sum. Default: `0`.\n\nBy default, the initial value of the sum is `0`. To choose a different one, use the `initialValue` option.\n\n```javascript\nvar pow = require( '@stdlib/math-base-special-pow' );\n\nvar out = sumSeries( geometricSeriesClosure( 0.5 ), {\n    'initialValue': 1\n});\n// returns 3\n\nfunction geometricSeriesClosure( x ) {\n    var exponent = -1;\n    return gen;\n\n    function gen() {\n        exponent += 1;\n        return pow( x, exponent );\n    }\n}\n```\n\nTo change the maximum number of terms to be summed, set the `maxTerms` option.\n\n```javascript\nvar pow = require( '@stdlib/math-base-special-pow' );\n\n// Note: infinite sum is 2\nvar out = sumSeries( geometricSeriesClosure( 0.5 ), {\n    'maxTerms': 10\n});\n// returns ~1.998\n\nfunction geometricSeriesClosure( x ) {\n    var exponent = -1;\n    return gen;\n\n    function gen() {\n        exponent += 1;\n        return pow( x, exponent );\n    }\n}\n```\n\nThe default tolerance of `2.22e-16` used to assess convergence can be changed via the `tolerance` option.\n\n```javascript\nvar pow = require( '@stdlib/math-base-special-pow' );\n\nvar out = sumSeries( geometricSeriesClosure( 0.5 ), {\n    'tolerance': 1e-3\n});\n// returns ~1.998\n\nfunction geometricSeriesClosure( x ) {\n    var exponent = -1;\n    return gen;\n\n    function gen() {\n        exponent += 1;\n        return pow( x, exponent );\n    }\n}\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.usage --\u003e\n\n\u003csection class=\"examples\"\u003e\n\n## Examples\n\n\u003c!-- eslint-disable no-restricted-syntax, node/no-unsupported-features/es-syntax --\u003e\n\n\u003c!-- eslint no-undef: \"error\" --\u003e\n\n```javascript\nvar log1p = require( '@stdlib/math-base-special-log1p' );\nvar sumSeries = require( '@stdlib/math-base-tools-sum-series' );\n\nfunction* log1pSeries( x ) {\n    var mMult = -x;\n    var mProd = -1;\n    var k = 0;\n    while ( true ) {\n        mProd *= mMult;\n        k += 1;\n        yield ( mProd / k );\n    }\n}\n\nconsole.log( 'log1p(0.5) evaluated via math-log1p module: %d', log1p( 0.5 ) );\nconsole.log( 'log1p(0.5) evaluated via infinite series expansion: %d', sumSeries( log1pSeries( 0.5 ) ) );\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.examples --\u003e\n\n\u003c!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. --\u003e\n\n\u003csection class=\"related\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.related --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\n\u003csection class=\"main-repo\" \u003e\n\n* * *\n\n## Notice\n\nThis package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.\n\nFor more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].\n\n#### Community\n\n[![Chat][chat-image]][chat-url]\n\n---\n\n## License\n\nSee [LICENSE][stdlib-license].\n\n\n## Copyright\n\nCopyright \u0026copy; 2016-2025. The Stdlib [Authors][stdlib-authors].\n\n\u003c/section\u003e\n\n\u003c!-- /.stdlib --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"links\"\u003e\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-tools-sum-series.svg\n[npm-url]: https://npmjs.org/package/@stdlib/math-base-tools-sum-series\n\n[test-image]: https://github.com/stdlib-js/math-base-tools-sum-series/actions/workflows/test.yml/badge.svg?branch=main\n[test-url]: https://github.com/stdlib-js/math-base-tools-sum-series/actions/workflows/test.yml?query=branch:main\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-tools-sum-series/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/math-base-tools-sum-series?branch=main\n\n\u003c!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/math-base-tools-sum-series.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/math-base-tools-sum-series/main\n\n--\u003e\n\n[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg\n[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im\n\n[stdlib]: https://github.com/stdlib-js/stdlib\n\n[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors\n\n[umd]: https://github.com/umdjs/umd\n[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules\n\n[deno-url]: https://github.com/stdlib-js/math-base-tools-sum-series/tree/deno\n[deno-readme]: https://github.com/stdlib-js/math-base-tools-sum-series/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/math-base-tools-sum-series/tree/umd\n[umd-readme]: https://github.com/stdlib-js/math-base-tools-sum-series/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/math-base-tools-sum-series/tree/esm\n[esm-readme]: https://github.com/stdlib-js/math-base-tools-sum-series/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/math-base-tools-sum-series/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-tools-sum-series/main/LICENSE\n\n[infinite-series]: https://en.wikipedia.org/wiki/Series_%28mathematics%29\n\n[es6-generator]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Statements/function*\n\n\u003c/section\u003e\n\n\u003c!-- /.links --\u003e\n","funding_links":["https://github.com/sponsors/stdlib-js","https://opencollective.com/stdlib","https://tidelift.com/funding/github/npm/@stdlib/stdlib"],"categories":[],"sub_categories":[],"project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fmath-base-tools-sum-series","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstdlib-js%2Fmath-base-tools-sum-series","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fmath-base-tools-sum-series/lists"}