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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=5, b₁>=-11/2

For fixed z and a₁=3/2, a₂=5, b₁=-11/2

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

Input Form

HypergeometricPFQ[{3/2, 5}, {-(11/2), 7/2}, z] == (1/(8316 z^2)) (362880 - 196560 z + 69804 z^2 - 19440 z^3 + 4680 z^4 - 1134 z^5 + 378 z^6 - 261 z^7 + 634 z^8 + 156 z^9 + 8 z^10) + (1/(16632 z^(5/2))) (E^z Sqrt[Pi] (-362880 + 438480 z - 257040 z^2 + 98280 z^3 - 27720 z^4 + 6174 z^5 - 1134 z^6 + 177 z^7 - 24 z^8 + 1416 z^9 + 320 z^10 + 16 z^11) 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]