Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9670)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9670.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, 21/4}, z] == (4 (2630323015778304000 - 1859525538889701375 Sqrt[z] + 5035841231323171500 z - 1324156289447376000 z^(3/2) + 3658371776175916800 z^2 - 679716325588608000 z^(5/2) + 2077321110036480000 z^3 - 511234728947712000 z^(7/2) + 2420303075617996800 z^4 + 151968671978618880 z^(9/2) - 634647193512837120 z^5 - 9586645967831040 z^(11/2) + 38955343392276480 z^6 + 208599515136000 z^(13/2) - 839436862488576 z^7 - 1694364598272 z^(15/2) + 6790343294976 z^8 + 4294967296 z^(17/2) - 17179869184 z^9 + E^(4 Sqrt[z]) (-2630323015778304000 - 1859525538889701375 Sqrt[z] - 5035841231323171500 z - 1324156289447376000 z^(3/2) - 3658371776175916800 z^2 - 679716325588608000 z^(5/2) - 2077321110036480000 z^3 - 511234728947712000 z^(7/2) - 2420303075617996800 z^4 + 151968671978618880 z^(9/2) + 634647193512837120 z^5 - 9586645967831040 z^(11/2) - 38955343392276480 z^6 + 208599515136000 z^(13/2) + 839436862488576 z^7 - 1694364598272 z^(15/2) - 6790343294976 z^8 + 4294967296 z^(17/2) + 17179869184 z^9)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (7120171570446309375 + 15773918556065670000 z + 12463343056644480000 z^2 + 7158432935098368000 z^3 + 10106022967197696000 z^4 - 2566609007542272000 z^5 + 156440929983528960 z^6 - 3362814437621760 z^7 + 27174258081792 z^8 - 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (7120171570446309375 + 15773918556065670000 z + 12463343056644480000 z^2 + 7158432935098368000 z^3 + 10106022967197696000 z^4 - 2566609007542272000 z^5 + 156440929983528960 z^6 - 3362814437621760 z^7 + 27174258081792 z^8 - 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (30659428191987302400 z^(9/2))

Standard Form

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MathML 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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]