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

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=5, b₁>=-11/2

For fixed z and a₁=9/2, a₂=5, b₁=-9/2

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

Input Form

HypergeometricPFQ[{9/2, 5}, {-(9/2), -(7/2)}, z] == (1/31255875) (31255875 + 44651250 z + 84199500 z^2 + 340540200 z^3 + 6810804000 z^4 - 416821204800 z^5 - 5873991177600 z^6 - 16063663392000 z^7 - 17488471069440 z^8 - 9667498406400 z^9 - 3059235486720 z^10 - 591982110720 z^11 - 72544604160 z^12 - 5699042304 z^13 - 284115840 z^14 - 8632576 z^15 - 144896 z^16 - 1024 z^17) - (1/31255875) (64 E^z Sqrt[Pi] (22855996800 z^(11/2) + 161750131200 z^(13/2) + 345770208000 z^(15/2) + 332704713600 z^(17/2) + 171417708000 z^(19/2) + 51952138560 z^(21/2) + 9776924640 z^(23/2) + 1175972040 z^(25/2) + 91202505 z^(27/2) + 4505640 z^(29/2) + 136008 z^(31/2) + 2272 z^(33/2) + 16 z^(35/2)) 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]