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

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=6, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{-(3/2), 6}, {-(11/2), -(5/2)}, z] == (1/779625) (779625 - 510300 z + 132300 z^2 + 100800 z^3 - 272160 z^4 + 604800 z^5 - 3104640 z^6 - 4325220 z^7 - 1740015 z^8 - 306208 z^9 - 26160 z^10 - 1056 z^11 - 16 z^12) + (1/1559250) (E^z Sqrt[Pi] (-9360540 z^(13/2) - 10140585 z^(15/2) - 3762570 z^(17/2) - 637560 z^(19/2) - 53360 z^(21/2) - 2128 z^(23/2) - 32 z^(25/2)) 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]