{"uid":"cap_rwEa3zDfG6YVx5zqsV-tP","slug":"numora-taylor-series-expansion-ba5f9fb3","name":"Numora Taylor Series Expansion","description":"100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.","url":"https://numomo.vercel.app/api/calculus/taylor","method":"POST","headers":{},"bodySchema":{"type":"object","required":["fn","order","center"],"properties":{"fn":{"type":"string"},"order":{"type":"integer"},"center":{"type":"number"}}},"responseSchema":{"type":"object","required":["success","result","computation"],"properties":{"result":{"type":"object","description":"Computation result varies by endpoint"},"success":{"type":"boolean","description":"Always true on success"},"computation":{"type":"string","description":"Human-readable description of what was computed"}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.1","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"registry","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.1/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_F8GFbxLcK2FJQOkAZ8ZTN","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","costPer":"request","priority":0,"asset":null,"unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes the Taylor series expansion of a mathematical function around a given center point up to a specified order","exampleAgentPrompt":"Compute the Taylor series expansion of sin(x) centered at 0 up to order 6 for me.","exampleUseCases":[{"title":"Physics simulation function approximation","prompt":"I need to approximate e^x near x=0 using a degree-4 Taylor polynomial — can you compute that expansion for me?"},{"title":"Numerical analysis of trigonometric function","prompt":"Expand cos(x) as a Taylor series centered at pi/2 up to order 5 so I can use it in my numerical solver."},{"title":"Engineering control system linearization","prompt":"Can you give me the 3rd-order Taylor series of ln(1+x) centered at 0? I need it to linearize a control system model."}],"resultDescription":"Returns a JSON object with a 'result' containing Taylor series coefficients and/or the polynomial expression, a 'success' boolean, and a 'computation' string describing what was computed in human-readable form.","failureModes":["Invalid or unparseable function expression string returns an error","Non-integer or negative order value causes validation failure","Expansion at a singularity of the function (e.g., ln(x) at x=0) may return an error or undefined result","Missing required fields (fn, order, center) result in a 400-level error","Payment failure via x402 protocol blocks request from being processed"],"whenToPreferThis":"Choose this endpoint when you need a pure server-side mathematical Taylor series computation without installing any local math library. Ideal for AI agents that need polynomial approximations of functions on-the-fly, for numerical analysis pipelines, physics simulations, or control system design where a symbolic or numeric Taylor expansion is required. Prefer this over general-purpose code execution when you want a lightweight, single-purpose calculus result with no setup overhead.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-16T00:49:57.732Z","isFirstParty":false}