Hundreds of thousands of mathematical results derived at Wolfram Research give the Wolfram Language unprecedented strength in the transformation and simplification of hypergeometric functions. This allows hypergeometric functions for the first time to take their place as a practical nexus between many special functions—and makes possible a major new level of algorithmic calculus.

Ordinary & Generalized Hypergeometric Functions

Hypergeometric2F1   ▪ HypergeometricPFQ   ▪ MeijerG   ▪ FoxH   ▪ BilateralHypergeometricPFQ

Confluent Hypergeometric Functions

Hypergeometric1F1   ▪ HypergeometricU   ▪ WhittakerM   ▪ WhittakerW   ▪ ParabolicCylinderD   ▪ Hypergeometric0F1

Regularized Hypergeometric Functions

Hypergeometric2F1Regularized   ▪ HypergeometricPFQRegularized   ▪ Hypergeometric1F1Regularized   ▪ Hypergeometric0F1Regularized

Multivariate Hypergeometric Functions

AppellF1   ▪ AppellF2   ▪ AppellF3   ▪ AppellF4

Related Tech Notes

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• Special Functions

Related Guides

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• Special Functions
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• Differential Equations

Related Links

• Demonstrations related to Hypergeometric Functions (Wolfram Demonstrations Project)