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

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=11/2, a₂>=11/2

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

For fixed z and a₁=11/2, a₂=6, b₁=-3/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(3/2), 1/2}, z] == (1/42525) (42525 - 1871100 z + 56756700 z^2 + 567567000 z^3 + 1216215000 z^4 + 1050269220 z^5 + 454201020 z^6 + 109160235 z^7 + 15328995 z^8 + 1274280 z^9 + 61152 z^10 + 1552 z^11 + 16 z^12) + (1/85050) (E^z Sqrt[Pi] (340540200 z^(5/2) + 1864863000 z^(7/2) + 3202699500 z^(9/2) + 2474444700 z^(11/2) + 1004917725 z^(13/2) + 232514415 z^(15/2) + 31874850 z^(17/2) + 2608200 z^(19/2) + 123840 z^(21/2) + 3120 z^(23/2) + 32 z^(25/2)) 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]