Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ant4)

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=-7/2

http://functions.wolfram.com/07.25.03.ant4.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(7/2), -(1/2)}, z] == (1/1488375) (1488375 + 28066500 z - 510810300 z^2 + 4540536000 z^3 - 69470200800 z^4 - 419026608000 z^5 - 662823907200 z^6 - 470130272640 z^7 - 179833996800 z^8 - 40611560640 z^9 - 5674047120 z^10 - 499773960 z^11 - 27584224 z^12 - 918720 z^13 - 16768 z^14 - 128 z^15) - (1/1488375) (4 E^z Sqrt[Pi] (41902660800 z^(9/2) + 158087311200 z^(11/2) + 210172611600 z^(13/2) + 136256904000 z^(15/2) + 49454533800 z^(17/2) + 10807320510 z^(19/2) + 1477803915 z^(21/2) + 128281770 z^(23/2) + 7008840 z^(25/2) + 231760 z^(27/2) + 4208 z^(29/2) + 32 z^(31/2)) 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]