{"uid":"cap_33AVi0JvDc65_aBoKsnxF","slug":"numora-taylor-series-expansion-api-dbef65d1","name":"Numora Taylor Series Expansion API","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://numormo.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_5VK64OJqJiP-jmuy-EOvr","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 specified center point up to a given order","exampleAgentPrompt":"Can you compute the Taylor series expansion of sin(x) centered at 0 up to order 6?","exampleUseCases":[{"title":"Physics simulation function approximation","prompt":"I need the Taylor expansion of e^x centered at 0 up to order 8 so I can use it as a polynomial approximation in my physics simulation."},{"title":"Calculus homework series check","prompt":"Can you expand cos(x) as a Taylor series centered at 0 to order 10 and show me the coefficients?"},{"title":"Numerical analysis near singular point","prompt":"Get me the Taylor series for ln(x) centered at x=1 up to order 5 — I need to approximate it near that point for a numerical integration problem."}],"resultDescription":"Returns a JSON object with a success flag, a result object containing the Taylor series coefficients and polynomial representation, and a human-readable computation description explaining what was computed.","failureModes":["Invalid or unparseable function expression in fn field — returns error","Order is negative or non-integer — returns validation error","Center point is at a singularity of the function (e.g. ln(x) at x=0) — returns computation error","Missing required fields fn, order, or center — returns 400-style error","Very high order requests may produce numerical precision issues"],"whenToPreferThis":"Choose this endpoint when you need server-side symbolic or numerical Taylor series computation without installing a math library. Ideal for AI agents that need polynomial approximations of functions on-the-fly, or when you want human-readable series expansion results with no external dependencies. Prefer over local computation when the agent environment lacks calculus libraries.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T18:31:37.342Z","isFirstParty":false}