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

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=4, a₂>=4

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

For fixed z and a₁=4, a₂=11/2, b₁=-9/2

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

Input Form

HypergeometricPFQ[{4, 11/2}, {-(9/2), -(9/2)}, z] == (1/2531725875) (2531725875 + 2750517000 z + 3648645000 z^2 + 8756748000 z^3 + 57891834000 z^4 + 3519823507200 z^5 + 172476163641600 z^6 + 843389366400000 z^7 + 1384655212281600 z^8 + 1071661491763200 z^9 + 457746413230080 z^10 + 117638826762240 z^11 + 19110847795200 z^12 + 2013354393600 z^13 + 138427146240 z^14 + 6124683264 z^15 + 167022592 z^16 + 2539520 z^17 + 16384 z^18) + (1/2531725875) (2048 E^z Sqrt[Pi] (12029472000 z^(11/2) + 181367424000 z^(13/2) + 624884803200 z^(15/2) + 869797958400 z^(17/2) + 614596248000 z^(19/2) + 248536512000 z^(21/2) + 61687332000 z^(23/2) + 9792601920 z^(25/2) + 1015479990 z^(27/2) + 69047400 z^(29/2) + 3030735 z^(31/2) + 82170 z^(33/2) + 1244 z^(35/2) + 8 z^(37/2)) 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]