Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.add1)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=3, b₁>=-11/2

For fixed z and a₁=1/2, a₂=3, b₁=-11/2

http://functions.wolfram.com/07.25.03.add1.01

Input Form

HypergeometricPFQ[{1/2, 3}, {-(11/2), 9/2}, z] == (-907200 + 241920 z - 68040 z^2 + 14451 z^3 - 2394 z^4 + 312 z^5 - 31 z^6 + 2 z^7)/(99 z^3) + (1/(198 z^(7/2))) (E^z Sqrt[Pi] (907200 - 846720 z + 390600 z^2 - 118080 z^3 + 26100 z^4 - 4440 z^5 + 591 z^6 - 60 z^7 + 4 z^8) Erf[Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]