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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 6}, {-(11/2), -(7/2)}, z] == (1/49116375) (49116375 + 38272500 z + 41674500 z^2 + 95256000 z^3 + 943034400 z^4 - 16345929600 z^5 + 299675376000 z^6 + 1983690777600 z^7 + 3227021164800 z^8 + 2293095006720 z^9 + 867051924480 z^10 + 192084076800 z^11 + 26207823360 z^12 + 2248014240 z^13 + 120623232 z^14 + 3901696 z^15 + 69120 z^16 + 512 z^17) + (1/49116375) (16 E^z Sqrt[Pi] (47177121600 z^(13/2) + 188708486400 z^(15/2) + 256005262800 z^(17/2) + 165947594400 z^(19/2) + 59519993400 z^(21/2) + 12762385920 z^(23/2) + 1704755475 z^(25/2) + 144153690 z^(27/2) + 7658760 z^(29/2) + 246000 z^(31/2) + 4336 z^(33/2) + 32 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]