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

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=11/2, b₁>=-11/2

For fixed z and a₁=11/2, a₂=11/2, b₁=-1/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(1/2), 4}, z] == -((1/(297675 z)) (4 E^(z/2) (-945 - 74790 z + 1161000 z^2 + 8975520 z^3 + 14490000 z^4 + 9045792 z^5 + 2579904 z^6 + 353280 z^7 + 22272 z^8 + 512 z^9) BesselI[0, z/2])) - (1/(297675 z^2)) (4 E^(z/2) (3780 + 1485 z + 7290 z^2 - 127080 z^3 + 2556000 z^4 + 8415792 z^5 + 6933024 z^6 + 2258496 z^7 + 331776 z^8 + 21760 z^9 + 512 z^10) BesselI[1, z/2])

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]