Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al1v)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=4, b₁>=-11/2

For fixed z and a₁=7/2, a₂=4, b₁=-11/2

http://functions.wolfram.com/07.25.03.al1v.01

Input Form

HypergeometricPFQ[{7/2, 4}, {-(11/2), -(7/2)}, -z] == (1/49116375) (49116375 - 35721000 z + 35721000 z^2 - 74844000 z^3 + 681080400 z^4 + 10897286400 z^5 + 185253868800 z^6 - 1111153075200 z^7 + 1630394438400 z^8 - 1034257029120 z^9 + 344097699840 z^10 - 65760952320 z^11 + 7529410560 z^12 - 520504320 z^13 + 21107712 z^14 - 458752 z^15 + 4096 z^16) - (1/49116375) ((512 Sqrt[Pi] (879076800 z^(13/2) - 3223281600 z^(15/2) + 3968773200 z^(17/2) - 2306329200 z^(19/2) + 730031400 z^(21/2) - 135331560 z^(23/2) + 15194655 z^(25/2) - 1036785 z^(27/2) + 41670 z^(29/2) - 900 z^(31/2) + 8 z^(33/2)) Erfi[Sqrt[z]])/E^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]