Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7vc)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7vc.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 23/4}, z] == (4 z^(1/4) (-43673516350088625 - 58231355133451500 Sqrt[z] + 9402782656176000 z - 194154819175699200 z^(3/2) + 21435158330127360 z^2 - 149990740019527680 z^(5/2) + 9376906058956800 z^3 - 94658022531072000 z^(7/2) - 27248223279513600 z^4 + 117790987308761088 z^(9/2) + 3272437395357696 z^5 - 13408729269534720 z^(11/2) - 110544606461952 z^6 + 445941622505472 z^(13/2) + 1269162835968 z^7 - 5089536245760 z^(15/2) - 4294967296 z^8 + 17179869184 z^(17/2) + E^(4 Sqrt[z]) (43673516350088625 - 58231355133451500 Sqrt[z] - 9402782656176000 z - 194154819175699200 z^(3/2) - 21435158330127360 z^2 - 149990740019527680 z^(5/2) - 9376906058956800 z^3 - 94658022531072000 z^(7/2) + 27248223279513600 z^4 + 117790987308761088 z^(9/2) - 3272437395357696 z^5 - 13408729269534720 z^(11/2) + 110544606461952 z^6 + 445941622505472 z^(13/2) - 1269162835968 z^7 - 5089536245760 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (43673516350088625 - 419265756960850800 z - 813121468045286400 z^2 - 619521118510694400 z^3 - 450560813462323200 z^4 + 480598201026478080 z^5 - 53961903273148416 z^6 + 1787557872402432 z^7 - 20371029884928 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (43673516350088625 - 419265756960850800 z - 813121468045286400 z^2 - 619521118510694400 z^3 - 450560813462323200 z^4 + 480598201026478080 z^5 - 53961903273148416 z^6 + 1787557872402432 z^7 - 20371029884928 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z])/(2286003421402103808 z^(19/4))

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]