Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ah1a)

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=-5/2

http://functions.wolfram.com/07.25.03.ah1a.01

Input Form

HypergeometricPFQ[{3/2, 5}, {-(5/2), -(3/2)}, z] == (1/135) (135 + 270 z + 2700 z^2 - 88200 z^3 - 595080 z^4 - 760716 z^5 - 363324 z^6 - 79575 z^7 - 8514 z^8 - 428 z^9 - 8 z^10) + (1/270) E^z Sqrt[Pi] (-463320 z^(7/2) - 1724580 z^(9/2) - 1822860 z^(11/2) - 798705 z^(13/2) - 167256 z^(15/2) - 17448 z^(17/2) - 864 z^(19/2) - 16 z^(21/2)) 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]