Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ald8)

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=5, b₁>=-11/2

For fixed z and a₁=7/2, a₂=5, b₁=-11/2

http://functions.wolfram.com/07.25.03.ald8.01

Input Form

HypergeometricPFQ[{7/2, 5}, {-(11/2), -(7/2)}, z] == (1/49116375) (49116375 + 44651250 z + 53581500 z^2 + 130977000 z^3 + 1362160800 z^4 - 24518894400 z^5 + 463134672000 z^6 + 3168192787200 z^7 + 5303763360000 z^8 + 3869338314240 z^9 + 1499552087040 z^10 + 340047590400 z^11 + 47440081920 z^12 + 4157059200 z^13 + 227693184 z^14 + 7512832 z^15 + 135680 z^16 + 1024 z^17) + (1/49116375) (64 E^z Sqrt[Pi] (18460612800 z^(13/2) + 75893630400 z^(15/2) + 105665893200 z^(17/2) + 70208434800 z^(19/2) + 25783569000 z^(21/2) + 5655341160 z^(23/2) + 772086735 z^(25/2) + 66676785 z^(27/2) + 3615360 z^(29/2) + 118440 z^(31/2) + 2128 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]