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

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=-9/2

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

Input Form

HypergeometricPFQ[{11/2, 6}, {-(9/2), -(5/2)}, z] == (1/200930625) (200930625 + 589396500 z + 2554051500 z^2 + 40864824000 z^3 - 1042053012000 z^4 + 26398676304000 z^5 + 252947316585600 z^6 + 581414362905600 z^7 + 582172713158400 z^8 + 312548964940800 z^9 + 99984640896000 z^10 + 20246433177600 z^11 + 2686624012800 z^12 + 237485122560 z^13 + 13987765440 z^14 + 539020800 z^15 + 12976128 z^16 + 176128 z^17 + 1024 z^18) + (1/200930625) (32 E^z Sqrt[Pi] (2399879664000 z^(11/2) + 13168570464000 z^(13/2) + 24552615024000 z^(15/2) + 22036904064000 z^(17/2) + 11091497508000 z^(19/2) + 3406471588800 z^(21/2) + 671445595800 z^(23/2) + 87468444000 z^(25/2) + 7632028845 z^(27/2) + 445343850 z^(29/2) + 17044440 z^(31/2) + 408240 z^(33/2) + 5520 z^(35/2) + 32 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]